Partial Orders in Regular Semigroups
K. V. R. Srinivas, Y. L. Anasuya · 2023
First we have obtained equivalent conditions for a regular semigroup and is equivalent to N = N1 It is observed that every regular semigroup is weakly separative and C \(\subseteq\) S and on a completely regular semigroup and is partial order. It is also obtained that a band (S,.) isnormaliffC = N. It is also observed that on a completely regular semigroup (S,),.C = S = N iff (S,.) islocally 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,.) isanormalband of groups then C = S = N.