Algebras of reducedE-Fountain semigroups and the generalized ample identity
Itamar Stein · Communications in Algebra · 2021
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:kS→kC (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.