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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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A commutativity theorem for rings
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by M. Chacron PDF
Proc. Amer. Math. Soc. 59 (1976), 211-216 Request permission

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.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 211-216
  • MSC: Primary 16A70
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0414636-1
  • MathSciNet review: 0414636