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is a CS-algebra
Author(s):
S.
K.
Jain;
P.
Kanwar;
S.
Malik;
J.
B.
Srivastava
Journal:
Proc. Amer. Math. Soc.
128
(2000),
397-400.
MSC (1991):
Primary 16S14, 13B21, 13C10, 13F05
Posted:
July 8, 1999
MathSciNet review:
1636958
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Additional information
Abstract:
In this paper, it is shown that the group algebra is right CS if and only if . Moreover, when , then is also CS as a module over its center.
References:
- 1.
- Nguyen Viet Dung, Dinh Van Huynh, Patrick F. Smith and Robert Wisbauer, Extending Modules, Pitman, London, 1994. MR 96f:16008
- 2.
- Irving Kaplansky, Commutative Rings, Allyn and Bacon, Inc., Boston, 1970. MR 40:7234
- 3.
- Joachim Lambek, Lectures on Rings and Modules, Blaisdell Publishing Company, London, 1966. MR 34:5857
- 4.
- J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Wiley-Interscience, NY, 1987. MR 89j:16023
- 5.
- Donald S. Passman, The Algebraic Structure of Group Rings, John Wiley, NY, 1977. MR 81d:16001
- 6.
- Donald S. Passman, Infinite Group Rings, Marcel Dekker, NY, 1971. MR 47:3500
- 7.
- Louis Rowen, Ring Theory, vol I, Academic Press, NY, 1988. MR 89h:16001
- 8.
- Oscar Zariski and Pierre Samuel, Commutative Algebra, vol. I, D. Van Nostrand, NY, 1958. MR 19:833e
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Additional Information:
S.
K.
Jain
Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701
Email:
jain@math.ohiou.edu
P.
Kanwar
Address at time of publication:
Division of Mathematics and Computer Science, Truman State University, Kirksville, Missouri 63501
Email:
pkanwar@math.ohiou.edu
S.
Malik
Affiliation:
Department of Mathematics, Hindu College, Delhi-110007, India
Email:
sbm@csec.ernet.in
J.
B.
Srivastava
Affiliation:
Department of Mathematics, Indian Institute of Technology, New Delhi-110016, India
Email:
jbsrivas@maths.iitd.ernet.in
DOI:
10.1090/S0002-9939-99-05095-9
PII:
S 0002-9939(99)05095-9
Keywords:
Group algebra,
CS-ring,
Dedekind domain
Received by editor(s):
April 10, 1998
Posted:
July 8, 1999
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1999,
American Mathematical Society
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