摘要
This article is based on the notions of a congruence of a semigroup and the p-lower and p-upper approximations of a nonempty subset of a semigroup, discussing some properties of the product of these two subsets according to the properties of some especial single subsets such as subsemigroups and ideals, then the rigorous proof was given. Thus the rough theory in semigroups are completed and perfected.
