Some Propositions About Inverse Semigroups

Abstract

Inverse semigroups are an important subclass of the class of semigroups. An important role in the properties of the semigroups in general and in the class of inverse semigroups in particular is played by the set of their idempotents, which we denote by E or ES for a semigroup S. In the first part of this paper we will show some propositions about left unitary, right unitary, unitary subsets and closed subsets in the inverse semigroups. We will also see some properties of the maximum idempotent - separating congruence in an inverse semigroup S and its connection with Clifford’s semigroups.

Received: 19 February 2024 / Accepted: 15 March 2024 / Published: 23 March 2024