Characterization of Chain As a Regular Semi Group

INTRODUCTION In [2,3], Semi group was established as a non-empty set S with binary operation * such that S is associative on * that is, for all a, b, c [member of] S, a*(b*c) = (a*b)*c. If there exist an element 1 of S such that for every a[member of] S, a*1 = 1*a = a. We say that 1 is an identity element of S and that S is a semi group with identity. If (S,*) has an additional property that ([for all]a, b [member of] S) ab = ba, we say that, it is a commutative semi group.