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

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.