A commutativity theorem for power-associative rings

Author:

Outcalt D. L.,Yaqub Adil

Abstract

Let R be a power-associative ring with identity and let I be an ideal of R such that R/I is a finite field and xy (mod I) implies x2 = y2 or both x and y commute with all elements of I. It is proven that R must then be commutative. Examples are given to show that R need not be commutative if various parts of the hypothesis are dropped or if “x2 = y2” is replaced by “xk = yk” for any integer k > 2.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference2 articles.

1. A generalization of Wedderburn's theorem;Outcalt;Proc. Amer. Math. Soc.,1967

2. A commutativity theorem for rings

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A commutativity theorem;Algebra Universalis;1980-12

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