Abstract
Let S be a reduced E-Fountain semigroup. If S satisfies the congruence condition, there is a natural construction of a category associated with S. We define a
-module homomorphism
(where
is any unital commutative ring). With some assumptions, we prove that
is an isomorphism of
-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.
Acknowledgments
The author thanks Professor Victoria Gould for a helpful conversation and the referee for helpful comments.