Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Central localizations of regular rings


Authors: E. P. Armendariz, Joe W. Fisher and Stuart A. Steinberg
Journal: Proc. Amer. Math. Soc. 46 (1974), 315-321
MSC: Primary 16A30
DOI: https://doi.org/10.1090/S0002-9939-1974-0352164-0
MathSciNet review: 0352164
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show that a ring $ R$ is von Neumann regular (or a $ V$-ring) if and only if every central localization of $ R$ at a maximal ideal of its center is von Neumann regular (or a $ V$-ring). Strongly regular rings are characterized by the property that all central localizations at maximal ideals of the center are division rings. Also we consider whether regular PI-rings can be characterized by the property that all central localizations at maximal ideals of the center are simple.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A30

Retrieve articles in all journals with MSC: 16A30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0352164-0
Keywords: Regular ring, strongly regular ring, $ V$-ring, PI-ring, fully idempotent ring, central localization
Article copyright: © Copyright 1974 American Mathematical Society