On three approaches to conjugacy in semigroups

TL;DR

This paper compares three different approaches to defining conjugacy in semigroups, analyzing their properties and relationships to understand their implications in algebraic structures.

Contribution

It provides a comparative analysis of three conjugacy notions in semigroups, highlighting their differences and potential applications.

Findings

The three approaches to conjugacy are formally defined and contrasted.

Relationships and distinctions among the conjugacy notions are clarified.

Implications for algebraic structure analysis are discussed.

Abstract

We compare three approaches to the notion of conjugacy for semigroups, the first one via the transitive closure of the $uv\sim vu$ relation, the second one via an action of inverse semigroups on themselves by partial transformations, and the third one via characters of finite-dimensional representations.