Prime injectivity of acts

Injectivity with respect to some special subclasses of monomorphisms in the category of acts has been studied. In this article, we define the notion of prime monomorphism and study $\mathcal{M}$-injectivity whenever $\mathcal{M}$ is a subclass of all prime monomorphisms. We investigate Skornjakov criterion with respect to prime injectivity of acts and characterize their behaviour of the property considered under well-known constructions such as product, coproduct, and direct sum.