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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Conditions for the commutativity of semigroups


Author: G. Kowol
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
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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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Article copyright: © Copyright 1976 American Mathematical Society