Classical prime injective S-acts

In this article, we define classical prime right ideals of semigroups and generalize them to classical prime subacts of acts. We study the notion of Μ-injectivity where Μ is the class of all classical prime monomorphisms. We investigate the Skornjakov criterion with respect to classical prime injectivity of acts. We characterize their behavior under well-known constructions such as the product, coproduct and direct sum. Among other results, it is proved that an S-act is classical prime injective if and only if it is a classical prime-absolute retract, if and only if it has no classical prime-essential extension.

کلیدواژه ها:

Classical prime ideal ، Classical prime subact ، Classical prime injective