Welcome to this Web page
Biography
Distinguished Professor S. K. Jain served Ohio
University, Department of
Mathematics from 1970 to 2009. He also served as Director of Center of Ring
Theory and its Applications from 2001 to 2009. Before joining the faculty at Ohio
University, he was a Reader in
Mathematics at the University of Delhi
(196570). Currently, he is an Advisor and Distinguished Adjunct Professor at King
Abdulaziz University,
Jeddah, SA.
Dr. Jain has held visiting professor appointments at several institutions
worldwide. His visiting positions include the Riverside,
Santa Barbara and Berkeley
campuses of the University of California,
the Ohio State
University in Columbus,
North Carolina State University in Raleigh,
University of Chicago,
McMaster University
in Hamilton and University
of Frankfurt, as well as the Indian
Statistical Institute, and the Indian Institute of Technology.
Dr. Jain has authored more than 135 research articles that have been
published in professional journals. His papers have appeared in the
Transactions of the American Mathematical Society, the Proceedings of the
American Mathematical Society, the Pacific Journal of Mathematics, Journal of
Algebra, Journal of Pure and Applied Algebra, Communications in Algebra, Archiv der Mathematik,
Math Zeitchrift, Linear Algebra and Applications,
Linear and Multilinear Algebra, SIAM J. Discrete
Methods, SIAM J. Matrix Analysis and Applications, etc. He has coauthored five
undergraduate/graduate texts. In particular, he is a coauthor of the widely
used graduate text Basic Abstract Algebra (second edition), published by
Cambridge University Press (1994), Linear Algebra: An Interactive Approach
published by Brooks/Cole (2003), graduate text entitled Topics
in Applied Abstract Algebra, published by the American Mathematical
Society (2008), and the book Cyclic
Modules and the Structure of Rings in the Oxford
Mathematical Monographs, Oxford University Press (2012).
In addition, Dr. Jain is a coeditor of seven
research volumes of scholarly papers in Ring Theory in Marcel Dekker (1977), Springer Verlag
(1990), World Scientific Press (1993), Birkhauser
(1997), American Math Society (2000), American Math Society (2006) and American
Math Society (2008). He is a two times recipient of Senior Scientist Fulbright
Award (199192, 199596), has been awarded grants by DAAD (German Academic Exchange
Service) and USIndia Scientific Exchange grants by the National Science
Foundation (199192, 199294). He was the recipient of a United Nations
Development Project Grant (199899), and of a conference grant from National
Security Agency (1999).
He was awarded the Outstanding Graduate Faculty Award,
1999 at Ohio University.
He has delivered Professional lectures at mathematical meetings all over the
world and has been the organizer of conferences on many topics in Abstract
Algebra.
He is an Executive Editor of the Journal of Algebra and its Applications, World
Scientific Press, and that of Bulletin of Mathematical Sciences, SpringerVerlag. He is also serving on the editorial board of
Electronic Journal of Algebra.
He has supervised 23 Ph.D. dissertations in Noncommutative
Rings, Modules, and Applied Linear Algebra. A life member of the Indian
Mathematical Society, he is also a member of the American Mathematical Society.
Publications
20152017

Algebras and semigroups of locally subexponential growth, submitted J.
Algebra ( with Alahmadi, Hamed and Zelmanov)

Quasipermutation singular matrices are products of idempotents. Linear
Algebra Appl. 496 (2016), 487–495
(with
Alahmadi
and Leroy)

Decompositions into products of idempotents. Electron.
J. Linear Algebra 29 (2015), 74–88
(with
Alahmadi,
Leroy, and Sathaye)

Characterizations of
almost selfinjective modules,
Noncommutative rings and their applications, 11–17, Contemp.
Math., 634, Amer.
Math. Soc., Providence, RI, 2015 (with Adel Alahmadi and Surjeet Singh)

Finite
generation of Lie algebras associated to associative algebras ,
J. Algebra 426 (2015), 69–78
(with
Adel Alahmadi,
Hamid Alsulami, and Efim Zelmanov)

Indecomposable
decomposition and couniserial dimension,
Bull. Math. Sci. 5 (2015), no.
1, 121–136 (with A Ghorbhani and Z. Nazemian)
20112014

Almost injective modules—a
brief survey.
J. Algebra Appl.
13 (2014),
1350164, 12 pp (with Adel Alahmadi)

Euclidean pairs and
quasiEuclidean rings.
J. Algebra
406 (2014),
154–170.
16Wxx
(with Adel Alahmadi, T.Y.Lam, and Andre Leroy)

Decomposition of singular
matrices into idempotents.
Linear Multilinear Algebra
62 (2014), no. 1, 13–27.
15A23
(with Adel Alahmadi
and Andre Leroy)

Structure of Leavitt path
algebras of polynomial growth.
Proc. Natl. Acad. Sci. USA
110 (2013), no. 38, 15222–15224.
16S99
(with Adel Alahmadi,
Hamid Alsulami, and Efim Zelmanov)

Monotonicity of Nonnegative Matrices, Linear and
Multilinear Algebra (2012), 855864 (with Adel
Alahmadi and Yousef
Alkhamees )

On
Semigroups and Semirings of Nonnegative Matrices, Linear and Multilinear
Algebra (2012),595598 (With Adel Alahmadi and Yousef
Alkhamees)

ADS
Modules, Journal of Algebra 352(2012), 215232 (with Adel Alahmadi and Andre
Leroy)

Leavitt
Path Algebras of Finite GelfandKirillov Dimension, Journal of Algebra and its
Applications,11(2012)1250225, 16 (with Adel Alahmadi, Hamed Alsulami, Efim
Zelmanov)

Perfect semiring of
nonnegative matrices. Combinatorial matrix theory and generalized inverses of
matrices, 177–181, Springer, New Delhi, 2013 (with Adel Alahmadi and
Yousef Alkhamees)

Decomposition of Singular Matrices into idempotents, Lineaqr
and Multinear Algebra, to appear (2013) (with Adel Alahmadi and Andre Leroy)

Cyclic Modules and the Structure of Rings (Oxgord Mathematical
Monographs), Oxford University Press (2013) (with Ashish Srivastava and Askar
Tuganbaev)
20082010
1. Direct Sums of Injective and Projective Modules,
Journal of Algebra, 324 (2010), 14291434 (with P. A. Guil
Asensio and Ashish K. Srivastava).
2. Erratum: Generalized Group Algebras of Locally
Compact Groups, Communications in Algebra, Volume 38, Issue
10 (2010), page 3974 (with A. I. Singh and Ashish K. Srivastava).
3. Rings over which cyclics
are direct sums of projective and CS or noetherian,
Glasgow J. Mathematics, 52, A (2010), 103110 (with C.
Holston and A. Leroy).
4. Nonnegative GroupMonotone Matrices and the Minus
Partial Order, Linear Algebra and Appl. 420 (2009),
121132 (with B. Blackwood).
5. A note on Almost Injective Modules,
Math J. Okayama Univ, 51 (2009), 101109 (with Adel Alahmadi).
6. On Sigmaq rings, J. Pure and Applied Algebra 213
(2009), 969976 (with Surjeet Singh and Ashish K. Srivastava).
7. Ore extensions and Vdomains, Rings, Modules and
Representations, Contemp. Math. Series
AMS, 480 (2009), 263288 (with T. Y. Lam and A. Leroy).
8. Shorted Operators Relative to a Partial
Order in a Regular Ring , Communications in Algebra,
Vol. 37, Number 11 (2009), 41414152 (with Ashish K. Srivastava, B. Blackwood and K. M. Prasad).
9. Generalized Group Algebras of Locally Compact
Groups, Communications in Algebra 36 (2008), 35593563 (with A. I. Singh and Ashish K. Srivastava).
10. New Characterizations of sigmainjective
Modules, Proc. Amer. Math. Soc. 316 (10), 2008, 34613466
(with K. I. Beidar and Ashish
K. Srivastava).
11. Essential Extensions of Direct Sum of
Simple ModulesII, Modules and Comodules, Trends in
Mathematics, Birkhauser 2008, 243246 (with Ashish K. Srivastava).
20052007
1. When is a Semilocal
Group Algebra Continuous, Journal of Algebra, 312, 2007, 152157 (with P. Kanwar and J. B. Srivastava).
2. Semiprime
CS Group Algebra of PolycyclicByFinite Group Without
Domains as Summands as Hereditary, J. Algebra, 307 (2007), 541546 (with Adel Alahamadi and J. B. Srivastava).
3. Essential Extensions of a Direct Sum of Simple Modules,
Contemporary Math Series, Groups, Rings and Algebras, 420, American Math
Society (2006), 1523 (with Ashish K.Srivastava and Late K.I.Beidar).
4. RightLeft Symmetry of Right Nonsingular Right
MaxMin CS Prime Rings, Coummunications Alg, 34, 11 (2006), 3883  3889 (with Husain
S. AlHazmi, Adel N. Alahmadi).
5. Group algebras in which the complements are
direct summands. (Russian) Fundamental and Applied Math 11 (2005), no. 3, 311
(with A. N. Alahmadi, Pramod
Kanwar, and J. B. Srivastava).
6. On generalized q.f.d.
modules. Arch. Math. (Brno) 41 (2005), no. 3, 243251 ( with
Mohammad Saleh and S. R. LopezPermouth
)
7. Modules which are invariant under monomorphisms
of their injective hulls, J. Australian Math. Soc., 79(2005),
349360 (with A. Alahmadi and N. Er).
8. Whens Is Every Module with Essentail Socle a Direct Sums of
Quasiinjectives?, Comm.
Algebra 33 (2005), no. 11, 42514258, (with K. Beidar).
20032004
1.Decomposition of Generalized
polynomial symmetric matrices, Linear Algebra and its Applications,
376(2004), 6983. (with R.B. Bapat
and John Tynan).
2.Survey of some recent results
in CS group algebras and Open Quesitons, Advances
in Algebra, World Scientific Press (2003), 401408. (with
P. Kanwar and Srivastava).
3.Nonnegative rank factorization
of a nonnegative matrix with A†A ≥ 0, Linear and Multilinear
Algebra, 51 (2003), 8395 (with John Tynan).
4.CS matrix rings over local
rings, J. Algebra,264 (2003), 251261. (with
K.I. Beidar, P. Kanwar and
J.B. Srivastava).
5.When cyclic singular modules
over a simple ring are injective, J. Algebra, 263(2003), 185192. (with D.V. Huynh and S.R. LopezPermouth).
6.Prime Goldie Rings of Uniform Dimension at Least Two and
with all Onesided Ideals CS are Semihereditary, Communications
in Algebra, 31(2003), no. 11, 53555360(with Dinh
V. Huynh and S.R. LopezPermouth).
7.The Structure of Right
Continuous Right pRings, Communications
in Algebra (2004), 32, no.
1, 315332 (with K. Beidar).
8.Semilocal CS Matrix rings of order > 1 over group
algebras of solvable groups are selfinjective, J. Algebra (2004), 275, no. 2, 856858
(with K. Beidar, Pramond Kanwar, and J. B. Srivastava).
9.Nonsingular CS Rings coincide
with Tight PPRings,J. Algebra,
282(2004), 626637 (with K. Beidar and P. Kanwar).
10.Nonnegative matrices A with
AA# ≥ 0, Linear Algebra and its Applications, 379(2004), 381194 (with J.
Tynan).
11.Modules which are invariant
under monomorphisms of their injective hulls, to
appear in J. Australian Math. Soc. (with A. Alahmadi and N. Er).
20002002
1.Column of Uniform Color in a
Rectangular Array with Rows Having Cyclically Reperated
Color Patterns, Discrete Math., 254(2002), 371392 (with S.R. Nagpaul).
2.An Example of a Right qring, Israel
J. Math. 127(2002) 303316 (with K. Beidar,
Y. Fong, and W.F. Ke).
3.Rings characterized by direct
sums of CS modules, Communications in Algebra 28(9) (2000), 42194222
(with Dinh V. Huynh and S.R. LopezPermouth).
4.Quotient rings of algebras of
functions and operators, Math Zeitchrift, 234
(2000) (4), 721737 (with A.I. Singh).
5. KD¥ is a
CSalgebra, Proc. Amer. Math Soc. 128(2000), 397400 (with P. Kanwar, S. Malik and J.B. Srivastava).
6.On the symmetry of the Goldie
and CS conditions for prime rings, Proc. Amer. Math Soc. 128 (2000),
31533157 (with D. Huynh and S.R. LopezPermouth).
7.Nonsingular semiperfect
CSrings II, Bull. London Math Soc., 32(2000), 421431 (with P. Kanwar and S.R.
LopezPermouth).
8.Design and implementation of an electric text for
Linear Algebra with Matlab drills, Proc 12th International
Conf. on Technology in Collegiate Math, Addison Welsely,
NY 135139 (2000) (with A.D. Gunawardena).
1999
1.Rings in which every (finitely
generated) right ideal is quasicontinuous, Glasgow J. Math 41 (1999),
167181 (with S.R. LopezPermouth and R. Syed).
2.Generalized power symmetric
stochastic matrices, Proc. Amer. Math Soc. 127 (1999) 19871994, (with
R.B. Bapat and K. Manju
Prasad).
1998
1.RightLeft symmetry of aRÅ bR=(a+b)R in von Neumann regular rings, J. Pure &
Applied Algebra, 133 (1998) 141142 (with K.M. Prasad).
2.On uniform dimensions of ideals
in right nonsingular rings, J. Pure and Applied Algebra, 133 (1998),
117140, (with T.Y. Lam and Andre Leroy).
3.Nonsingular semiperfect
CSrings, J. Alg, 203 (1998), 361373, (with S.Brthwal, P. Kanwar and S.
LopezPermouth).
1997
1. Weighted MoorePenrose inverse of a
Boolean Matrix, Linear Algebra and Applications, 255 (1997),
267279(with R. Bapat and T. Pati).
2. Nonnegative idempotent matrices and
the minus partial order, Linear Algebra and Applications, 261 (1997)
143154, (with R. Bapat and L. Snyder).
4. Rings of Morita context in which each right ideal is
weakly selfinjective, Advances in Ring Theory, Birkhauser
3138 (1997), (with S. Barthwal, S. Jhingan, and S. LopezPermouth).
1996
1. On weakly injective continuous
modules, Lecture Notes in Pure and Applied Math on Abelian
Groups and Modules, Volume 182, Marcel Dekker,
(1996) 385392.
2. A note on 0,1  matrices, Linear
and Multilinear Algebra, 41 (3) (1996), 193198
(with L. Snyder).
3. When is simple ring noetherian?, J. Algebra, 184 (1996), 784794 (with
D. Huynh and S.R. LopezPermouth).
4. On Gbased partial order extensions, SIAM J. Matrix
Analysis & Applications, 17 (4) (1996), 834850. (with
S.K. Mitra and Hans Werner).
5. Mutual injective hulls, Canadian Math. Bull., 39 (1), (1996), 6873 (with
S.R. LopezPermouth and R. Syed).
6. On a class of nonnoetherian
Vrings, Communications in Algebra, 34 (9) (1996), 28392850 (with D.
Huynh and S.R. LopezPermouth).
7.Application of Near Rings to Balanced Incomplete Block Designs, Applied
Abstract Algebra, Center for Professional Development in Higher Education,
Univ. Delhi, Delhi (1996), 1218 (with K. Bala
Subramanian).
8. Applications of Burnside and Polya Theorems,
Applied Abstract Algebra, Center for Professional Development in Higher
Education, Univ. Delhi, Delhi
(1996), 1937 (with M. Srinivasan).
9. An Application of Finite Fields and Number Theory to Cryptography,
Applied Abstract Algebra, Center for Professional Development in Higher
Education, Univ. Delhi, Delhi (1996), 96100 (with L.R. Vermani).
1995
1. Weakly injective modules over hereditary noetherian prime rings, Journal Australian Math. Soc., 58 Series (4) 287297 (with
S.R. LopezPermouth).
2. Superfluous Covers, Communications in Algebra,
23 (5) (1995), 16631677 (with S.R. LopezPermouth
and L. Rowen).
1994
1. On weakly projective and
weakly injective modules, Canadian J. Math, 46 (5), (1994), 971981
(with S.R.LopezPermouth, K. Oshiro
and M. Saleh).
2. Roots of symmetric idempotent Boolan
matrices, SIAM Proceedings, Fifth Linear Algebra Conference (1994),
389393 (with R.B. Bapat).
3. A survey of theory of weakly
injective modules, Computational Algebra, Marcel Dekker,
N.Y. (1994) 205 232. (with S.R. LopezPermouth).
1993
1. Nonnegative normal matrices, Linear
Algebra & Applications 182 (1993), 147155. (with
L. Snyder).
2. On weakly projective modules,
Ring Theory, World Scientific Press, N.J. (1993) 20028. (with S. LopezPermouth & M. Saleh).
1992
1. Rings whose cyclics
have finite Goldie dimension, Journal of Algebra, 153 (1992), 3740.
(with A. AlHuzali and S.R.
LopezPermouth).
2. On a class of QIrings, Glasgow Journal Math.,
34 (1992), 7581. (with S.R. LopezPermouth
and S. Singh).
3. On weaklyinjective modules and rings, Osaka J.
Mathematics 29 (1992), 7588. (with S.R. LopezPermouth and A. AlHuzali).
4. On weaklyinjective modules (expository article), Math Student, 58
(1992), 14.
1991
1. A characterization of uniserial rings via continuous and discrete modules, Journal
Australian Math Soc., 60 (1991), 197203. (with
S.R. LopezPermouth and S.T. Rizvi).
2. Modified iterative methods for consistent linear
systems, Linear Algebra and Applications, (1991), 123143. (with A. Gunawardena and L.
Snyder).
1990
1. Continuous rings with acc on
essentials are artinian, Proc. Amer. Math Soc.,
108 (1990), 583586. (with S.R. LopezPermouth and S.T. Rizvi).
2. Rings whose cyclic are essentially
embeddable in projective modules, Journal of Algebra, 128 (1990),
257269. (with S.R. LopezPermouth).
3. On weak monotonocity
of the powers of nonnegative matrices, Linear and Multilinear
Algebra, 26 (1990), 223230. (with A. Gunawardena and L. Snyder).
4. On the weak relativeinjectivity
of rings and modules, Noncommutative Ring
Theory, Lecture Notes in Mathematics No. 1448, SpringerVerlag,
Heidelberg Berlin  New York (1990), 9398. (with A.
AlHuzali and S.R. LopezPermouth).
1989
1. A generalization of the Wedderburn  Artin theorem,
Proc. Amer. Math Soc., 106 (1989) 1023. (with
S.R. LopezPermouth).
2. Periodicity of the graph of
nonnegative matrices, Linear Algebra and Applications, 120 (1989),
181192. (with A. Gunawardena
and L. Snyder).
3. Generalizations of QFrings, and continuous and discrete modules,
(expository), The Math Student, 57 (1989), 219224.
1988
1. Finite uniserial
rings of finite characteristic, Communications in Algebra 16 (10), 1988,
21332135. (with J. Luh
and B. ZimmermannHuisgen).
2. Nonnegative generalized inverses of
powers of nonnegative matrices, Linear Algebra and Applications 107
(1988), 169179. (with A. Berman).
1987
1. Rings whose (proper) cyclic modules have cyclic p injective hulls, Archiv
der Math 48, (1987), 109115. (with
H. Saleh).
2. Rings with finitely generated injective
(quasiinjective) hulls of cyclic modules, Communications in Algebra 15
(1987), 16791687.
3. Rings, Fields and Vector Spaces, Encyclopedia of
Physical Sciences and Technology Vol. 12, Academic Press (1987), 209221.
4. New Classes of monotone matrices, Current Trends in
Matrix Theory, Elsevier Sc. Pub. (1987), 155156. (with
L. Snyder).
1985
1. qHypercyclis Rings,
Canadian J. Math. v. 37 (1985), 452466. (with
D.S. Malik).
1984
1. Over determined linear systems
satisfying nonnegativity constraints, Linear
Algebra and Applications, 57 (1984), 205213.
2. Linear systems having nonnegative
least Squares solutions, Linear and Multilinear
Algebra, 15 (1984), 121132. (with L.
Snyder).
3. Linear Systems having nonnegative best approximate solutions, Algebra
and Applications, Marcel Dekkar (1984), 99132.
1983
1. Remarks on prime valuation rings, Proc. International Conference of
Math., Pecasse Euroset,
Maastricht, Netherland
(1983), 111112.
1982
1. Nonnegative rectangular matrices having certain
nonnegative wweighted group inverses, Proc. Amer. Math. Soc. 85 (1982),
19.
2. Nonnegative minimum norm least squares solutions of
Ax=B, J.I.M.S. 46 (1982), 8589. (with L.
Snyder).
3. Nonnegative matrices A such that Ax=b has nonnegative
best approximate solution, SIAM Journal Algebraic and Discrete Methods,
3 (1982), 197213. (with Y. Egawa).
1981
1. Semiperfect rings whose
cyclic modules are continuous, Archiv der Math. 37 (1981), 140143. (with
B. Mueller).
2. Nonnegative l
monotone matrices, SIAM J. Algebraic and Discrete Methods 2 (1981),
6676. (with L. Snyder).
1980
1. Nonnegative matrices having
nonnegative Drazin pseudoinverses, Linear Algebra
and Applications, 29 (1980), 173183. (with
V.K. Goel).
2. Decomposition of nonnegative groupmonotone matrices,
Trans, Amer. Math. Soc., 257 (1980), 371385. (with
V.K. Goel and E. Kwak).
1979
1. Nonnegative mth roots
of nonnegative 0symmetric idempotent matrices, Linear Algebra and its
Applications, 23 (1979), 3751. (with V.K. Goel and E. Kwak).
2. Nonnegative matrices having same Moore Penrose and
group inverses, Linear and Multilinear Algebra 7
(1979), 5972. (with V.K. Goel
and E. Kwak).
1978
1. Rings whose cyclic modules are continuous, Journal
Indian Math. Soc. 42 (1978), 197202.(with S.
Mohammed).
2. p
injective modules and rings whose cyclic are pinjective,
Communications in Algebra 6 (1978), 5972. (with
V.K. Goel).
3. Nonnegative matrices having nonnegative generalized in
verses (expository), The Math. Student 46 (1978),4248.
1977
1. Nonnegative Matrices A with A^{t}=A^{m}. Bull
International Statistical Inst., 47 (1977), 256259.
2. Semiprime
rings having finite length w.r.t. an idempotent
kernel functor, Israel J. Math, 28 (1977)
110112. (with S. Singh).
3. Rings and Modules of fractions w.r.t. an
idempotent kernel functor (expository), The Math. Student 45 (1977).
4. Rings whose cyclic modules have
certain properties and the duals, Ring Theory: Lecture Notes Series in Pure
and Applied Math., Marcel Dekker, v. 25 (1977),
143160.
1976
1. Semiperfect
rings with quasiprojective left ideals, Math Journal Okayama University,
19 (1976), 3943. (with S. Goel).
2. Rings whose proper cyclic modules are quasiinjective,
Pacific J. Math. 67 (1976), 461472. (with R.G. Symonds and S. Singh).
1975
1. On quasiinjective and
pseudoinjective modules, Canadian Math. Bull. 18 (1975), 359366. (with S. Singh).
2. Rings whose cyclic modules are injective or projective,
Proc. Amer. Math. Soc. 53 (1975), 1618. (with S. Goel and S. Singh).
3. Rings with quasiprojective left ideals, Pacific J.
Math. 60 (1975), 169181. (with S. Singh).
4. Rings with a Polynomial Identity.
1971
1. Prime rings having onesided ideal
with polynomial identity coincide with Special Johnson rings, Journal of
Algebra, 19 (1971), 125130.
2. Restricted regular rings, Mathematische Zeitschrift,
121 (1971), 5154. (With S. Jain).
3. Selfinjective group rings, Archiv
der Math. 22 (1971), 5354.
1970
1. A note on the adjoint group of a ring, Archiv
der Math. 21 (1970), 366368. (with
P.B. Bhattacharya).
2. Rings having solvable adjoint
groups, Proc. Amer. Math. Soc. 25 (1970), 563565. (with
P.B. Bhattacharya).
1969
1. Rings having onesided ideal satisfying a polynomial
identity, Archiv der
Math. 20 (1969), 1723. (with S. Singh).
2. Rings in which each right ideal is quasiinjective,
Pacific J. Math. 31 (1969), 7380. (with S.
Mohammed and S. Singh).
3. A note on the generalized
commutative rings, Journal Indian Math. Soc. 33 (1969), 16. (with P.K. Menon).
1968
1. Prime rings having onesided ideal satisfying a
polynomial identity, Pacific J. Math. 24 (1968), 421424.
2. Rings with polynomial constraint, Journal Indian
Math. Soc. 32 (1968), 7987. (with L.P. Belluce).
1967
1. On pseudoinjective modules
and self pseudoinjective rings, Journal Math. Sc. 2 (1967), 2331. (with S. Singh).
1966
1. Polynomial rings with a pivotal monomial, Proc.
Amer. Math. Soc. 17 (1966), 942945.
2. A remark on primitive rings with Jpivotal monomial,
Journal Math. Sc. 1 (1966), 5961.(with L.P. Belluce).
3. Generalized commutative rings, Nagoya Math. Journal,
27 (1966), 15. (with I.N. Herstein
and L.P. Belluce).
4. Rings with constraints (Expository), The Math.
Student 34 (1966), 174178.
1964
1. On unitary and p
unitary rings, Publications mathematicae, Debrecen (1964), 241244.
Books
 First Course in Group Theory,
Halsted Press, John Wiley, N.Y. (1972)
 First Course in Rings and
Fields, Halsted Press, John Wiley, N.Y. (1977)
 First Course in Linear
Algebra, Halsted Press, John Wiley & Sons,
N.Y. (1983). Reprinted by New Age Press, India (1995)
 Basic Abstract Algebra,
*Second Revised Edition, Cambridge University Press, LondonNew York,
1994. (with P.B. Bhattacharya and S.R. Nagpaul)
*First Edition, 1986 and Reprinted 1989.
 Ring Theory (Edited), Lecture
Notes in Pure and Applied Mathematics, v. 25, Marcel Dekker,
N.Y. (1977).
 Noncommutative
Ring Theory (Edited), Lecture Notes in Mathematics No. 1448, SpringerVerlag, HeidelbergBerlin New York, (1990). (with
S.R. LopezPermouth) .
 Ring Theory (Edited), World
Scientific Press, N.J.,(1993). (with S.T. Rizvi).
 Applied Abstract Algebra (Edited),
Center for Professional Development in Higher Education, University of
Delhi (1996).
 Advances in Ring Theory
(Edited),Birkhauser (1997). (with S.T. Rizvi)
 Algebra and its Applications,
Contemporary Mathematics 259(2000) (coedited
with D. Huynh and S.R. LopezPermouth).
 Linear Algebra: An
Interactive Approach, Brooks/Cole (2003). (with A.D. Gunawardena)
 Topics in Applied Abstract
Algebra, Brooks/Cole (2005). (with S.R. Nagpaul)
 Algebra and its Applications,
Contemporary Mathematics 419 (2006) (coedited
with D. Huynh and S.R. LopezPermouth).
 Noncommutative
Rings, Group Rings, Diagram Algebras and their Applications, Contemporary
Mathematics (2008) (coedited with S. Parvathi).
Number of Ph.D Dissertations Directed = 23
last updated: 1/12/2007