Weakly Abundant Semigroups and variants

TL;DR

This paper explores variants of weakly U abundant semigroups, demonstrating that their idempotent variants retain the property and analyzing the natural partial order within these structures.

Contribution

It introduces the concept of variants of weakly U abundant semigroups and proves that their idempotent variants are also weakly U abundant, expanding understanding of their structural properties.

Findings

Idempotent variants of weakly U abundant semigroups are also weakly U abundant.

The natural partial order on variants of these semigroups is characterized.

Generalized Green's relations are used to define and analyze the semigroups.

Abstract

A weakly U abundant is a class of semigroups characterized using some generalized Green' relations. In this paper we discuss the variants of weakly U - abundant semigroups and it is shown that the idempotent variants of these semigroups are again weakly U abundant. Further we also discuss the natural partial order on variants of a weakly U abundant semigroup.