%0 Journal Article %T Properties of products for flatness in the category of $S$-posets %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Khosravi, Roghaieh %A Sedaghatjoo, Mojtaba %D 2016 %\ 07/01/2016 %V 5 %N 1 %P 131-152 %! Properties of products for flatness in the category of $S$-posets %K Product %K pomonoid %K $S$-poset %K Flat %K Condition$(WP)$ %K Condition $(PWP)$ %R %X 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. %U https://cgasa.sbu.ac.ir/article_15362_7f22a056e8b06f79525763eef82d6fa0.pdf