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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 (1965-70). 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 125 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 co-authored five
undergraduate/graduate texts. In particular, he is a co-author 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), and a recent graduate text entitled Topics
in Applied Abstract Algebra, published by Brooks/Cole (2005).
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 (1991-92, 1995-96), has
been awarded grants by DAAD (German Academic Exchange Service) and US-India
Scientific Exchange grants by the National Science Foundation (1991-92,
1992-94). He was the recipient of a United Nations Development Project Grant
(1998-99), 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 Bulletin of Mathematical Sciences, Springer-Verlag. 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
and the Society for Industrial and Applied Mathematics.
Publications
ARTICLES
2008-2010
1. Direct Sums of Injective and Projective Modules, Journal of Algebra, 324 (2010), 1429-1434 (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), 103-110 (with C. Holston and A. Leroy).
4. Nonnegative
Group-Monotone Matrices and the Minus Partial Order, Linear Algebra and Appl. 420 (2009), 121-132 (with B.
Blackwood).
5. A note on
Almost Injective Modules, Math J. Okayama Univ, 51 (2009), 101-109 (with
Adel Alahmadi).
6. On Sigma-q rings, J. Pure and Applied Algebra 213 (2009), 969-976 (with Surjeet Singh and Ashish K. Srivastava).
7. Ore extensions and V-domains, Rings, Modules and Representations, Contemp. Math. Series AMS, 480 (2009), 263-288 (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), 4141-4152 (with Ashish K. Srivastava, B. Blackwood and K. M. Prasad).
9. Generalized
Group Algebras of Locally Compact Groups, Communications in
Algebra 36 (2008), 3559-3563 (with A. I. Singh and Ashish K. Srivastava).
10. New Characterizations of sigma-injective
Modules, Proc. Amer. Math. Soc. 316 (10), 2008, 3461-3466 (with K. I. Beidar and Ashish K. Srivastava).
11. Essential Extensions of Direct Sum of Simple
Modules-II, Modules and Comodules, Trends in Mathematics,
Birkhauser 2008, 243-246 (with Ashish K. Srivastava).
2005-2007
1. When is a Semilocal Group Algebra Continuous,
Journal of Algebra, 312, 2007, 152-157 (with P. Kanwar and J. B. Srivastava).
2. Semiprime
CS Group Algebra of Polycyclic-By-Finite Group Without
Domains as Summands as Hereditary, J. Algebra, 307 (2007), 541-546 (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), 15-23 (with Ashish K.Srivastava and Late K.I.Beidar).
4. Right-Left Symmetry of Right Nonsingular Right
Max-Min CS Prime Rings, Coummunications Alg, 34, 11 (2006), 3883 - 3889 (with
Husain S. Al-Hazmi, Adel N. Alahmadi).
5. Group algebras in which the complements are
direct summands. (Russian) Fundamental and Applied Math 11 (2005), no. 3, 3--11
(with A. N. Al-ahmadi, Pramod Kanwar, and J. B. Srivastava).
6. On generalized q.f.d. modules. Arch. Math.
(Brno) 41 (2005), no. 3, 243--251 ( with Mohammad Saleh and S. R.
Lopez-Permouth )
7. Modules which are invariant under monomorphisms
of their injective hulls, J. Australian Math. Soc., 79(2005), 349-360 (with A. Alahmadi and N. Er).
8. Whens Is Every Module with Essentail Socle a Direct Sums of
Quasi-injectives?, Comm.
Algebra 33 (2005), no. 11, 4251--4258, (with K. Beidar).
2003-2004
1.Decomposition of Generalized
polynomial symmetric matrices, Linear Algebra and its Applications,
376(2004), 69-83. (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), 401-408. (with P. Kanwar and Srivastava).
3.Nonnegative rank factorization of
a nonnegative matrix with A†A ≥ 0, Linear and Multilinear
Algebra, 51 (2003), 83-95 (with John Tynan).
4.CS matrix rings over local
rings, J. Algebra,264 (2003), 251-261. (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), 185-192. (with
D.V. Huynh and S.R. Lopez-Permouth).
6.Prime Goldie Rings of Uniform Dimension at Least Two and
with all One-sided Ideals CS are Semihereditary, Communications
in Algebra, 31(2003), no. 11, 5355-5360(with Dinh
V. Huynh and S.R. Lopez-Permouth).
7.The Structure of Right
Continuous Right p-Rings, Communications
in Algebra (2004), 32, no.
1, 315-332 (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, 856-858
(with K. Beidar, Pramond Kanwar, and J. B. Srivastava).
9.Nonsingular CS Rings coincide
with Tight PP-Rings,J. Algebra,
282(2004), 626-637 (with K. Beidar and P. Kanwar).
10.Nonnegative matrices A with
AA# ≥ 0, Linear Algebra and its Applications, 379(2004), 381-194 (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).
2000-2002
1.Column of Uniform Color in a
Rectangular Array with Rows Having Cyclically Reperated
Color Patterns, Discrete Math., 254(2002), 371-392 (with S.R. Nagpaul).
2.An Example of a Right q-ring, Israel
J. Math. 127(2002) 303-316 (with K. Beidar, Y.
Fong, and W.-F. Ke).
3.Rings characterized by direct
sums of CS modules, Communications in Algebra 28(9) (2000), 4219-4222
(with Dinh V. Huynh and S.R. Lopez-Permouth).
4.Quotient rings of algebras of
functions and operators, Math Zeitchrift, 234
(2000) (4), 721-737 (with A.I. Singh).
5. KD¥ is a
CS-algebra, Proc. Amer. Math Soc. 128(2000), 397-400 (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),
3153-3157 (with D. Huynh and S.R. Lopez-Permouth).
7.Nonsingular semiperfect
CS-rings II, Bull. London Math Soc., 32(2000), 421-431 (with P. Kanwar and S.R. Lopez-Permouth).
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 135-139 (2000) (with A.D. Gunawardena).
1999
1.Rings in which every (finitely
generated) right ideal is quasi-continuous, Glasgow J. Math 41 (1999),
167-181 (with S.R. Lopez-Permouth and R. Syed).
2.Generalized power symmetric
stochastic matrices, Proc. Amer. Math Soc. 127 (1999) 1987-1994, (with
R.B. Bapat and K. Manju
Prasad).
1998
1.Right-Left symmetry of aRÅ bR=(a+b)R in von Neumann regular rings, J. Pure &
Applied Algebra, 133 (1998) 141-142 (with K.M. Prasad).
2.On uniform dimensions of ideals
in right nonsingular rings, J. Pure and Applied Algebra, 133 (1998), 117-140,
(with T.Y. Lam and Andre Leroy).
3.Nonsingular semiperfect
CS-rings, J. Alg, 203 (1998), 361-373, (with S.Brthwal, P. Kanwar and S.
Lopez-Permouth).
1997
1. Weighted Moore-Penrose inverse of a
Boolean Matrix, Linear Algebra and Applications, 255 (1997),
267-279(with R. Bapat and T. Pati).
2. Nonnegative idempotent matrices and
the minus partial order, Linear Algebra and Applications, 261 (1997)
143-154, (with R. Bapat and L. Snyder).
4. Rings of Morita context in which each right ideal is
weakly self-injective, Advances in Ring Theory, Birkhauser
31-38 (1997), (with S. Barthwal, S. Jhingan, and S. Lopez-Permouth).
1996
1. On weakly injective continuous
modules, Lecture Notes in Pure and Applied Math on Abelian
Groups and Modules, Volume 182, Marcel Dekker,
(1996) 385-392.
2. A note on 0,1 - matrices, Linear
and Multilinear Algebra, 41 (3) (1996), 193-198
(with L. Snyder).
3. When is simple ring noetherian?, J. Algebra, 184 (1996), 784-794 (with
D. Huynh and S.R. Lopez-Permouth).
4. On G-based partial order extensions, SIAM J. Matrix
Analysis & Applications, 17 (4) (1996), 834-850. (with S.K. Mitra and Hans Werner).
5. Mutual injective hulls, Canadian Math. Bull., 39
(1), (1996), 68-73 (with S.R. Lopez-Permouth and R. Syed).
6. On a class of nonnoetherian
V-rings, Communications in Algebra, 34 (9) (1996), 2839-2850 (with D.
Huynh and S.R. Lopez-Permouth).
7.Application of Near Rings to Balanced Incomplete Block Designs, Applied
Abstract Algebra, Center for Professional Development in Higher Education,
Univ. Delhi, Delhi (1996), 12-18 (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), 19-37 (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), 96-100 (with L.R. Vermani).
1995
1. Weakly injective modules over hereditary noetherian prime rings, Journal Australian Math. Soc.,
58 Series (4) 287-297 (with S.R. Lopez-Permouth).
2. Superfluous Covers, Communications in Algebra,
23 (5) (1995), 1663-1677 (with S.R. Lopez-Permouth
and L. Rowen).
1994
1. On weakly projective and
weakly injective modules, Canadian J. Math, 46 (5), (1994), 971-981
(with S.R.Lopez-Permouth, K. Oshiro
and M. Saleh).
2. Roots of symmetric idempotent Boolan
matrices, SIAM Proceedings, Fifth Linear Algebra Conference (1994),
389-393 (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. Lopez-Permouth).
1993
1. Nonnegative normal matrices, Linear
Algebra & Applications 182 (1993), 147-155. (with L. Snyder).
2. On weakly projective modules,
Ring Theory, World Scientific Press, N.J. (1993) 200-28. (with S. Lopez-Permouth & M. Saleh).
1992
1. Rings whose cyclics
have finite Goldie dimension, Journal of Algebra, 153 (1992), 37-40.
(with A. Al-Huzali and S.R. Lopez-Permouth).
2. On a class of QI-rings, Glasgow Journal Math.,
34 (1992), 75-81. (with S.R. Lopez-Permouth and S.
Singh).
3. On weakly-injective modules and rings, Osaka J.
Mathematics 29 (1992), 75-88. (with S.R. Lopez-Permouth
and A. Al-Huzali).
4. On weakly-injective modules (expository article), Math Student, 58
(1992), 1-4.
1991
1. A characterization of uniserial rings via continuous and discrete modules, Journal
Australian Math Soc., 60 (1991), 197-203. (with S.R. Lopez-Permouth and S.T. Rizvi).
2. Modified iterative methods for consistent linear
systems, Linear Algebra and Applications, (1991), 123-143. (with A. Gunawardena and L. Snyder).
1990
1. Continuous rings with acc on
essentials are artinian, Proc. Amer. Math Soc.,
108 (1990), 583-586. (with S.R. Lopez-Permouth
and S.T. Rizvi).
2. Rings whose cyclic are essentially
embeddable in projective modules, Journal of Algebra, 128 (1990),
257-269. (with S.R. Lopez-Permouth).
3. On weak monotonocity
of the powers of nonnegative matrices, Linear and Multilinear
Algebra, 26 (1990), 223-230. (with A. Gunawardena
and L. Snyder).
4. On the weak relative-injectivity
of rings and modules, Noncommutative Ring
Theory, Lecture Notes in Mathematics No. 1448, Springer-Verlag,
Heidelberg Berlin - New York (1990), 93-98. (with A. Al-Huzali
and S.R. Lopez-Permouth).
1989
1. A generalization of the Wedderburn - Artin theorem,
Proc. Amer. Math Soc., 106 (1989) 10-23. (with S.R. Lopez-Permouth).
2. Periodicity of the graph of
nonnegative matrices, Linear Algebra and Applications, 120 (1989),
181-192. (with A. Gunawardena and L. Snyder).
3. Generalizations of QF-rings, and continuous and discrete modules,
(expository), The Math Student, 57 (1989), 219-224.
1988
1. Finite uniserial
rings of finite characteristic, Communications in Algebra 16 (10), 1988,
2133-2135. (with J. Luh and B. Zimmermann-Huisgen).
2. Nonnegative generalized inverses of
powers of nonnegative matrices, Linear Algebra and Applications 107
(1988), 169-179. (with A. Berman).
1987
1. Rings whose (proper) cyclic modules have cyclic p- injective hulls, Archiv
der Math 48, (1987), 109-115. (with H. Saleh).
2. Rings with finitely generated injective
(quasi-injective) hulls of cyclic modules, Communications in Algebra 15
(1987), 1679-1687.
3. Rings, Fields and Vector Spaces, Encyclopedia of
Physical Sciences and Technology Vol. 12, Academic Press (1987), 209-221.
4. New Classes of monotone matrices, Current Trends in Matrix
Theory, Elsevier Sc. Pub. (1987), 155-156. (with L. Snyder).
1985
1. q-Hypercyclis Rings,
Canadian J. Math. v. 37 (1985), 452-466. (with D.S. Malik).
1984
1. Over determined linear systems
satisfying nonnegativity constraints, Linear
Algebra and Applications, 57 (1984), 205-213.
2. Linear systems having nonnegative
least Squares solutions, Linear and Multilinear
Algebra, 15 (1984), 121-132. (with L. Snyder).
3. Linear Systems having nonnegative best approximate solutions, Algebra
and Applications, Marcel Dekkar (1984), 99-132.
1983
1. Remarks on prime valuation rings, Proc. International Conference of
Math., Pecasse Euroset,
Maastricht, Netherland (1983), 111-112.
1982
1. Nonnegative rectangular matrices having certain
nonnegative w-weighted group inverses, Proc. Amer. Math. Soc. 85 (1982),
1-9.
2. Nonnegative minimum norm least squares solutions of
Ax=B, J.I.M.S. 46 (1982), 85-89. (with L. Snyder).
3. Nonnegative matrices A such that Ax=b has nonnegative
best approximate solution, SIAM Journal Algebraic and Discrete Methods,
3 (1982), 197-213. (with Y. Egawa).
1981
1. Semiperfect rings whose
cyclic modules are continuous, Archiv der Math. 37 (1981), 140-143. (with B. Mueller).
2. Nonnegative l
-monotone matrices, SIAM J. Algebraic and Discrete Methods 2 (1981),
66-76. (with L. Snyder).
1980
1. Nonnegative matrices having
nonnegative Drazin pseudo-inverses, Linear Algebra
and Applications, 29 (1980), 173-183. (with V.K. Goel).
2. Decomposition of nonnegative group-monotone matrices,
Trans, Amer. Math. Soc., 257 (1980), 371-385. (with V.K. Goel and E. Kwak).
1979
1. Nonnegative mth roots
of nonnegative 0-symmetric idempotent matrices, Linear Algebra and its
Applications, 23 (1979), 37-51. (with V.K. Goel
and E. Kwak).
2. Nonnegative matrices having same Moore -Penrose and
group inverses, Linear and Multilinear Algebra 7
(1979), 59-72. (with V.K. Goel and E. Kwak).
1978
1. Rings whose cyclic modules are continuous, Journal
Indian Math. Soc. 42 (1978), 197-202.(with S. Mohammed).
2. p
-injective modules and rings whose cyclic are p-injective,
Communications in Algebra 6 (1978), 59-72. (with V.K. Goel).
3. Nonnegative matrices having nonnegative generalized in-
verses (expository), The Math. Student 46 (1978),42-48.
1977
1. Nonnegative Matrices A with A^{t}=A^{m}. Bull
International Statistical Inst., 47 (1977), 256-259.
2. Semiprime
rings having finite length w.r.t. an idempotent
kernel functor, Israel J. Math, 28 (1977)
110-112. (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),
143-160.
1976
1. Semiperfect
rings with quasi-projective left ideals, Math Journal Okayama University,
19 (1976), 39-43. (with S. Goel).
2. Rings whose proper cyclic modules are quasi-injective,
Pacific J. Math. 67 (1976), 461-472. (with R.G. Symonds
and S. Singh).
1975
1. On quasi-injective and
pseudo-injective modules, Canadian Math. Bull. 18 (1975), 359-366. (with
S. Singh).
2. Rings whose cyclic modules are injective or projective,
Proc. Amer. Math. Soc. 53 (1975), 16-18. (with S. Goel
and S. Singh).
3. Rings with quasi-projective left ideals, Pacific J.
Math. 60 (1975), 169-181. (with S. Singh).
4. Rings with a Polynomial Identity.
1971
1. Prime rings having one-sided ideal
with polynomial identity coincide with Special Johnson rings, Journal of
Algebra, 19 (1971), 125-130.
2. Restricted regular rings, Mathematische Zeitschrift,
121 (1971), 51-54. (With S. Jain).
3. Self-injective group rings, Archiv
der Math. 22 (1971), 53-54.
1970
1. A note on the adjoint group of a ring, Archiv
der Math. 21 (1970), 366-368. (with P.B.
Bhattacharya).
2. Rings having solvable adjoint
groups, Proc. Amer. Math. Soc. 25 (1970), 563-565. (with P.B.
Bhattacharya).
1969
1. Rings having one-sided ideal satisfying a polynomial
identity, Archiv der
Math. 20 (1969), 17-23. (with S. Singh).
2. Rings in which each right ideal is quasi-injective, Pacific
J. Math. 31 (1969), 73-80. (with S. Mohammed and S. Singh).
3. A note on the generalized
commutative rings, Journal Indian Math. Soc. 33 (1969), 1-6. (with P.K. Menon).
1968
1. Prime rings having one-sided ideal satisfying a
polynomial identity, Pacific J. Math. 24 (1968), 421-424.
2. Rings with polynomial constraint, Journal Indian
Math. Soc. 32 (1968), 79-87. (with L.P. Belluce).
1967
1. On pseudo-injective modules
and self pseudo-injective rings, Journal Math. Sc. 2 (1967), 23-31.
(with S. Singh).
1966
1. Polynomial rings with a pivotal monomial, Proc.
Amer. Math. Soc. 17 (1966), 942-945.
2. A remark on primitive rings with J-pivotal monomial,
Journal Math. Sc. 1 (1966), 59-61.(with L.P. Belluce).
3. Generalized commutative rings, Nagoya Math. Journal,
27 (1966), 1-5. (with I.N. Herstein and L.P. Belluce).
4. Rings with constraints (Expository), The Math.
Student 34 (1966), 174-178.
1964
1. On unitary and p
-unitary rings, Publications mathe-maticae, Debrecen
(1964), 241-244.
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, London-New 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, Springer-Verlag, Heidelberg-Berlin- New York, (1990). (with S.R. Lopez-Permouth) .
- 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. Lopez-Permouth).
- 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. Lopez-Permouth).
- 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