Construction of Inverse Unit Regular Monoids from a Semilattice and a Group

Sreeja V.K

doi:10.14419/ijet.v7i4.36.24927

Abstract

This paper is a continuation of a previous paper [6] in which the structure of certain unit regular semigroups called R-strongly unit regular monoids has been studied. A monoid S is said to be unit regular if for each element s Î S there exists an element u in the group of units G of S such that s = sus. Hence where su is an idempotent and is a unit. A unit regular monoid S is said to be a unit regular inverse monoid if the set of idempotents of S form a semilattice. Since inverse monoids are R unipotent, every element of a unit regular inverse monoid can be written as s = eu where the idempotent part e is unique and u is a unit. Here we give a detailed study of inverse unit regular monoids and the results are mainly based on [10]. The relations between the semilattice of idempotents and the group of units in unit regular inverse monoids are better identified in this case. .

Highlights

Throughout this paper let E (= E(S)) denote the semilattice of idempotents and G (= G(S)) denote the group of units of S.Proposition 1.1 ([4])
Let S be an inverse monoid with G = G(S) and E = E(S)
It is well known that the set of idempotents E(S) of an inverse semigroup S is a semilattice

Summary

Introduction

Throughout this paper let E (= E(S)) denote the semilattice of idempotents and G (= G(S)) denote the group of units of S.Proposition 1.1 ([4]). Throughout this paper let E (= E(S)) denote the semilattice of idempotents and G (= G(S)) denote the group of units of S. S is unit regular if and only if for each s S there is an idempotent x E and g G such that s = xg. Let S be an inverse monoid with G = G(S) and E = E(S).

Results

Conclusion