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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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Conditions for the commutativity of semigroups
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by G. Kowol PDF
Proc. Amer. Math. Soc. 56 (1976), 85-88 Request permission

Abstract:

Let $S$ be a semigroup. Then by a theorem of Tully [7]: $S$ is a commutative semigroup iff $ab = {b^n}{a^m}$ for all $a,b \in S$ ($m,n \geqslant 1$, fixed). We prove the following: $S$ is a commutative semigroup iff $ab = {b^{n(a,b)}}{a^{m(a,b)}}$ for all $a,b \in S$, where one of the exponents $n(a,b)$ and $m(a,b)$ is constant and the other is independent of $a$ or $b$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 85-88
  • MSC: Primary 20M10
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0404492-X
  • MathSciNet review: 0404492