Document Type : Original Manuscript
Authors
1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
3 Department of Mathematics, Hakim Sabzevary University, Sabzevar, Iran.
Abstract
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
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