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Articles

Algebras of reduced E-Fountain semigroups and the generalized ample identity

Pages 2557-2570 | Received 25 Apr 2021, Accepted 22 Nov 2021, Published online: 16 Dec 2021
 

Abstract

Let S be a reduced E-Fountain semigroup. If S satisfies the congruence condition, there is a natural construction of a category C associated with S. We define a k-module homomorphism φ:kSkC (where k is any unital commutative ring). With some assumptions, we prove that φ is an isomorphism of k-algebras if and only if some weak form of the right ample identity holds in S. This gives a unified generalization for a result of the author on right restriction E-Ehresmann semigroups and a result of Margolis and Steinberg on the Catalan monoid.

2020 MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgments

The author thanks Professor Victoria Gould for a helpful conversation and the referee for helpful comments.

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