Residual Finiteness of Finitely Generated Quasi-commutative Semigroups

A semigroup S is called residually finite if for any pair of distinct elements a,b∈S, there exists a congruence P on S such that S/p is finite and （a,b） P. In1958, Malcev proved the following theorem: Any finitely generated abelian semigroupis residually finite . In this paper,we prove that a finitely generated quasi-commu-tative semigroup is residually finite. It generalizes the above theorem.