@article { author = {Khosravi, Roghaieh and Sedaghatjoo, Mojtaba}, title = {Properties of products for flatness in the category of $S$-posets}, journal = {Categories and General Algebraic Structures with Applications}, volume = {5}, number = {1}, pages = {131-152}, year = {2016}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {}, abstract = {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.}, keywords = {Product,pomonoid,$S$-poset,Flat,Condition$(WP)$,Condition $(PWP)$}, url = {https://cgasa.sbu.ac.ir/article_15362.html}, eprint = {https://cgasa.sbu.ac.ir/article_15362_7f22a056e8b06f79525763eef82d6fa0.pdf} }