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On a generalisation of self-injective von Neumann regular rings
Author(s):
George
Ivanov
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1051-1060.
MSC (1991):
Primary 16D50, 16D70;
Secondary 16E60
MathSciNet review:
1307533
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Abstract:
Apart from von Neumann regular rings, rings with infinite identities have not been studied in any detail. We take a first step in that direction by obtaining structure theorems for a class of self-injective rings with infinite identities. These extend the main structure theorems for self-injective von Neumann regular rings.
References:
- [F1]
- C. Faith, Lectures on Injective Modules and Quotient Rings, Lecture Notes in Mathematics 49 (1967). MR 37:2791
- [F2]
- ------, Algebra II. Ring Theory, Springer-Verlag, New York, 1976. MR 55:383
- [G]
- K.R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979. MR 80e:16011
- [I1]
- G. Ivanov, Non-local rings whose ideals are quasi-injective, Bull. Aust. Math. Soc. 6 (1972), 45--52. MR 45:311
- [I2]
- G. Ivanov, Rings with quasi-injective ideals, Bull. Aust. Math. Soc. 50 (1994), 197--204. CMP 95:02
- [J]
- S. K. Jain, Rings whose cyclic modules have certain properties and the duals, Lecture Notes Series 25 (1976), 143--160.
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Additional Information:
George
Ivanov
Affiliation:
Department of Mathematics, Macquarie University, Sydney, Australia 2109
Email:
ivanov@mpce.mq.edu.au
DOI:
10.1090/S0002-9939-96-03185-1
PII:
S 0002-9939(96)03185-1
Received by editor(s):
June 7, 1994
Received by editor(s) in revised form:
October 18, 1994
Additional Notes:
Honorary Associate at Macquarie University.
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1996,
American Mathematical Society
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