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On commutative idempotent rings

Published online by Cambridge University Press:  14 November 2011

R. R. Andruszkiewicz  and
E. R. Puczyłowski
R. R. Andruszkiewicz
Affiliation:
Institute of Mathematics, University of Warsaw, Białystok Division, Akademicka 2, 15-267 Białystok, Poland
E. R. Puczyłowski
Affiliation:
Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
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Abstract

We study the problem when a ring which is an extension of a commutative idempotent ring by a commutative idempotent ring is commutative. In particular, we answer Sands' question showing that the class of commutative idempotent rings whose every homomorphic image has zero annihilator is a maximal but not the largest radical class consisting of commutative idempotent rings.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 2 , 1995 , pp. 341 - 349
Copyright
Copyright © Royal Society of Edinburgh 1995

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References

1Gordon, R. and Robson, J. C.. Krull dimension, Mem. Amer. Math. Soc. 133 (Providence, R.I.: American Mathematical Society, 1973).Google Scholar
2Lanski, C.. Gabriel dimension and rings with involution. Houston Math. J. 4 (1978), 397–415.Google Scholar
3Sands, A. D.. Some subidempotent radicals. Colloq. Math. Soc. Janos Bolyai 61, Theory of Radicals, pp. 239–48 (Amsterdam: North Holland, 1993).Google Scholar