Document Type : Original Manuscript

Authors

• H. Rasouli ¹
• Gh. R. Moghaddasi ²
• N. Sarvghad ³

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

• prime sub $S$-poset
• regular prime monomorphism
• regular prime injective