PROPERTIES OF REGULAR SEMIGROUPS

Abstract

In this paper we proved that a regular semigroup (S,.) is µ -Inverse then it is E – Inverse. It is also proved that (S,.) is left regular semigroup it is GC- Commutative semigroup and left permutable. In the same way if (S,.) be a commutative left regular and left zero semigroup then S is H-commutative if it is regular. On the other hand (S,.) be completely regular semigroup then (S,.)is H-commutative if (s,.) is Externally Commutative left Zero Semigroup. It is also observe that a semigroup (S,.) with different properties satisfies some equivalent conditions of regular semigroup. The motivation to prove the theorems in this paper due to results J.M.Howie[2] and P.Srinivasulu Reddy, G.Shobhalatha[3].