On right $\pi$-inverse ordered semigroups

TL;DR

This paper introduces and characterizes right π-inverse ordered semigroups, exploring their structure, decomposition, and relationships with generalized Green's relations in the context of semilattices.

Contribution

It defines new classes of ordered semigroups and provides their structural characterizations and interrelations, expanding the theoretical understanding of π-inverse semigroups.

Findings

Semilattice decomposition of left π-t-simple ordered semigroups

Characterizations of right π-inverse ordered semigroups

Relationships between Green's relations and semilattice structures

Abstract

Here we introduce the notion of (left, right) $\pi$-$t$-simple, right $\pi$-inverse ordered semigroups and discuss characterizations and relationships concerning them. Semilattice decomposition of left $\pi$-$t$-simple ordered semigroups has been given here. Furthermore, we study an interrelation between the generalized Green's relations and the class of semigroups which are semilattices of right $\pi$-$t$-simple ordered semigroups.