ON REGULAR PRIME INJECTIVITY OF S-POSETS

In this paper, we define the notion of regular prime monomorphism for S-posets over a pomonoid S and investigate some categorical properties including products, coproducts and pullbacks. We study mathcal{M}-injectivity in the category of S-posets where mathcal{M} is the class of regular prime monomorphisms and show that the Skornjakov criterion fails for the regular prime injectivity. Considering a weaker form of such kind of injectivity, we obtain some classifications for pomonoids.

Keywords:

prime sub S-poset , regular prime monomorphism , regular prime injective