
TL;DR
This paper characterizes and constructs a class of semigroups called left equalizer simple semigroups, focusing on their algebraic properties and the structure of related semigroup algebras and congruences.
Contribution
It provides a characterization and construction method for left equalizer simple semigroups, expanding understanding of their algebraic structure and associated ideals.
Findings
Characterization of left equalizer simple semigroups
Construction methods for these semigroups
Analysis of related semigroup algebra ideals
Abstract
In this paper we characterize and construct semigroups whose right regular representation is a left cancellative semigroup. These semigroups will be called left equalizer simple semigroups. For a congruence on a semigroup , let denote the ideal of the semigroup algebra which determines the kernel of the extended homomorphism of onto induced by the canonical homomorphism of onto . We examine the right colons in general, and in that special case when has the property that the factor semigroup is left equalizer simple.
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