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.