Properties of products for flatness in the category of $S$-posets

Document Type : Research Paper


1 Department of Mathematics, Fasa University, Fasa, Iran.

2 Department of Mathematics, College of Science, Persian Gulf University, Bushehr, Iran.


This paper is devoted to the study of products of classes of right $S$-posets possessing one of the flatness properties and preservation of such properties under products. Specifically, we characterize a pomonoid $S$ over which its nonempty products as right $S$-posets satisfy some known flatness properties. Generalizing this results, we investigate products of right $S$-posets satisfying Condition $(PWP)$. Finally, we investigate pomonoids over which products of right $S$-posets transfer an arbitrary flatness property, projectivity, freeness, and regularity to their components.


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