Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A commutativity theorem for rings

Author: M. Chacron
Journal: Proc. Amer. Math. Soc. 59 (1976), 211-216
MSC: Primary 16A70
MathSciNet review: 0414636
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ R$ be any associative ring. Suppose that for every pair $ ({a_1},{a_2}) \in R \times R$ there exists a pair $ ({p_1},{p_2})$ such that the elements $ {a_i} - a_i^2{p_i}({a_i})$ commute, where the $ {p_i}$'s are polynomials over the integers with one (central) indeterminate. It is shown here that the nilpotent elements of $ R$ form a commutative ideal $ N$, and that the factor ring $ R/N$ is commutative. This result is obtained by the use of the concept of cohypercenter of a ring $ R$, which concept parallels the hypercenter of a ring.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A70

Retrieve articles in all journals with MSC: 16A70

Additional Information

PII: S 0002-9939(1976)0414636-1
Keywords: Commutator, polynomials, quasi-regular elements, subgroups preserved re quasi-inner automorphisms
Article copyright: © Copyright 1976 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia