ON RIGHT INVERSE $\Gamma$-SEMIGROUP

Let S = fa; b; c; : : : g and ? = f ; ; ; : : : g be two nonempty sets. S is called a ?-semigroup if a b 2 S, for all 2 ? and a; b 2 S and (a b) c = a (b c), for all a; b; c 2 S and for all ; 2 ?. An element e 2 S is said to be -idempotent for some 2 ? if e e = e. A ?- semigroup S is called regular ?-semigroup if each element of S is regular i.e, for each a 2 S there exists an element x 2 S and there exist ; 2 ? such that a = a x a. A regular ?-semigroup S is called a right inverse ?-semigroup if for any - idempotent e and -idempotent f of S, e f e = f e. In this paper we introduce ip - congruence on regular ?-semigroup and ip - congruence pair on right inverse ?-semigroup and investigate some results relating this pair.