Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-17T04:31:49.528Z Has data issue: false hasContentIssue false
  • English
  • Français

A commutativity theorem for rings

Published online by Cambridge University Press:  17 April 2009

Hiroaki Komatsu ,
Tsunekazu Nishinaka  and
Hisao Tominaga
Hiroaki Komatsu
Affiliation:
Department of Mathematics, Okayama University Okayama 700, Japan
Tsunekazu Nishinaka
Affiliation:
Department of Mathematics, Okayama University Okayama 700, Japan
Hisao Tominaga
Affiliation:
Department of Mathematics, Okayama University Okayama 700, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove the following theorem: Let R be a ring, l a positive integer, and n a non-negative integer. If for each x, y ∈ R, either xy = yx or xy = xn f(y)x1 for some f(X) ∈ X2Z[X], then R is commutative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 3 , December 1991 , pp. 387 - 389
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bell, H.E., ‘Commutativity results for semigroups in rings’, Proc. Internal. Sympos. Semigroup Theory, Kyoto (1990), 31–39.Google Scholar
[2]Komatsu, H. and Tominaga, H., ‘Chacron's condition and commutativity theorems’, Math. J. Okayama Univ. 31 (1989), 101–120.Google Scholar
[3]Komatsu, H. and Tominaga, H., ‘Some commutativity conditions for rings with unity’, Resultate Math. 10 (1991), 83–88.CrossRefGoogle Scholar