Ideal Extension and Idempotents of a Rees Matrix Semigroup

Abstract

This paper deals with the method of resolving two relvent problems of Rees matrix semigroups, the ideal extension problem and the structure of sandwich set of idempotents. To resolve the first problem let us consider the ideal extension of Rees matrix semigroup over the multiplicative group $ U(n). $ The study is done using the Rees matrix semigroup containing only the zero element and a semigroup which has more than one element. The idempotents of Rees matrix semigroup is studied using Biordered set and finally we arrive at a conclusion about the structure of sandwich set of idempotents.