Global determinism of completely regular semigroups

TL;DR

This paper proves that the class of all completely regular semigroups is globally determined, meaning semigroups with isomorphic global structures are themselves isomorphic, extending previous related results in semigroup theory.

Contribution

It establishes that completely regular semigroups are globally determined, generalizing earlier findings and contributing to the understanding of semigroup structure determination.

Findings

The class of completely regular semigroups is globally determined.

Global isomorphism implies semigroup isomorphism within this class.

Extends previous results on semigroup global determinability.

Abstract

The power semigroup of a semigroup $ S $ is the semigroup of all nonempty subsets of $ S $ equipped with the naturally defined multiplication. A class $\mathcal{K} $ of semigroups is globally determined if any two members of $ \mathcal{K} $ with isomorphic globals are themselves isomorphic. The global determinability for various classes of semigroups has attracted some attention during the past 50 years. In this paper we prove that the class of all completely regular semigroups is globally determined. This is an extension and generalization of a series of related results obtained by some other mathematicians.