Abstract

First we have obtained equivalent conditions for a regular semi-group and is equivalent to N = N1 It is observed that every regular semigroup is weakly separative and C ⊆ S and on a completely reg-ular semigroup S ⊆ N and S is partial order. It is also obtained that a band (S,.) is normal iff C = N. It is also observed that on a completely regular semigroup (S,.), C = S = N iff (S,.) is locally inverse semigroup and the restriction of C to E(S) is the usual partial order on E(S). Finally it is obtained that, if (S,.) is a normal band of groups then C = S = N. Key Words: Locally inverse semigroup, orthodox semigroup, completely regular semigroup, normal band.