Let M be a Г-semigroup. For a prime ideal I of M, let δI be the relation on M consisted of the pairs (x, y), where x and y are elements of M such that either both x and y are elements of I or both x and y are not elements of I. Let N be the semilattice congruence on M defined by xNy if and only if the filters of M generated by x and y coincide. Then the set N is the intersection of the relations δI , where I runs over the prime ideals of M. if R, L, I, H are the Green's relations of M and A the set of right ideals, B the set of left ideals and I the set of ideals of M, then we have H ⊆ R ⊆ I ⊆ N, H ⊆ L ⊆ I ⊆ N and L0 R ⊆ I.