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Proceedings of the American Mathematical Society

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

 
 

 

The potential $\mathcal {J}$-relation and amalgamation bases for finite semigroups


Authors: T. E. Hall and Mohan S. Putcha
Journal: Proc. Amer. Math. Soc. 95 (1985), 361-364
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9939-1985-0806071-4
MathSciNet review: 806071
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Abstract: Let $S$ be a finite semigroup, $a,b \in S$. When does there exist a finite semigroup $T$ containing $S$ such that $a\mathcal {J}b$ in $T$? This problem was posed to the second named author by John Rhodes in 1974. We show here that if $a$, $b$ are regular, then such a semigroup $T$ exists if and only if either $a\mathcal {J}b$ in $S$, or $a \notin SbS$ and $b \notin SaS$. We use this result to show that analgamation bases for the class of finite semigroups have linearly ordered $\mathcal {J}$-classes.


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Article copyright: © Copyright 1985 American Mathematical Society