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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a generalisation of self-injective von Neumann regular rings
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by George Ivanov PDF
Proc. Amer. Math. Soc. 124 (1996), 1051-1060 Request permission

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
  • Carl Faith, Lectures on injective modules and quotient rings, Lecture Notes in Mathematics, No. 49, Springer-Verlag, Berlin-New York, 1967. MR 0227206
  • Carl Faith, Algebra. II, Grundlehren der Mathematischen Wissenschaften, No. 191, Springer-Verlag, Berlin-New York, 1976. Ring theory. MR 0427349
  • K. R. Goodearl, von Neumann regular rings, Monographs and Studies in Mathematics, vol. 4, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. MR 533669
  • G. Ivanov, Non-local rings whose ideals are all quasi-injective, Bull. Austral. Math. Soc. 6 (1972), 45–52. MR 291217, DOI 10.1017/S0004972700044245
  • G. Ivanov, Rings with quasi-injective ideals, Bull. Aust. Math. Soc. 50 (1994), 197–204.
  • 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
  • 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 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 1051-1060
  • MSC (1991): Primary 16D50, 16D70; Secondary 16E60
  • DOI: https://doi.org/10.1090/S0002-9939-96-03185-1
  • MathSciNet review: 1307533