Hostname: page-component-669899f699-ggqkh Total loading time: 0 Render date: 2025-04-26T04:04:59.398Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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