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On the Commutativity of a Ring with Identity

Published online by Cambridge University Press:  20 November 2018

Jingcheng Tong
Jingcheng Tong*
Affiliation:
Department of Mathematics, Wayne State University, Detroit, MI 48202, USA Institute of Mathematics, Academia Sinica, Peking, China
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Abstract

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Let R be a ring with identity. R satisfies one of the following properties for all x, y ∈ R:

  1. (I) xynxmy = xm+1yn+1 and mnm! n! x≠0 except x = 0;

  2. (II) xynxm = xm + 1yn + 1 and mm! n! x≠0 except x = 0;

  3. (III) xmyn = ynxm and m! n! x≠0 except x = 0;

  4. (IV) (xpyQ)n = xpnyqn for n = k, k + 1 and N(p, q, k) x≠0 except x = 0, where N(p, q, k) is a definite positive integer. Then R is commutative.

Keywords

16A70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 456 - 460
Copyright
Copyright © Canadian Mathematical Society 1984

References

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