2024/04/11 by Stein, Itamar · 1 citation
#16G10 #20M20 #20M25 #20M30 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2404.08075
With every reduced E-Fountain semigroup S which satisfies the generalized right ample condition we associate a category with zero morphisms C(S). Under some assumptions we prove an isomorphism of \Bbbk-algebras \Bbbk S≃\Bbbk0C(S) between the semigroup algebra and the contracted category algebra where \Bbbk is any commutative unital ring. This is a simultaneous generalization of a former result of the author on reduced E-Fountain semigroups which satisfy the congruence condition, a result of Junying Guo and Xiaojiang Guo on strict right ample semigroups and a result of Benjamin Steinberg on idempotent semigroups with central idempotents. The applicability of the new isomorphism is demonstrated with two well-known monoids which are not members of the above classes. The monoid of order-preserving functions on an n-set and the monoid of binary relations with demonic composition.