CONSTRUCTION OF UNIT REGULAR MONOIDS

Abstract

Let G be the group of units of a monoid S. A unit regular semigroup S  should satisfy the condition that corresponding to each   there should exist an element  such that  . Consider     as the set  of non units of S. Then  evidently  is a regular sub semigroup of S. Then   Conversely starting from a regular semigroup So and a group G we have constructed a unit regular semigroup with  S with G as group of units of S  and as semigroup of non-units of S. .