ON REGULAR PRIME INJECTIVITY OF S-POSETS

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 M-injectivity in the category of S-posets where 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

Journal of Algebraic Systems
Volume 8, Issue 2
January 2021
Pages 219-230

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