@article { author = {Khosravi, Roghaieh and Liang, Xingliang}, title = {On (po-)torsion free and principally weakly (po-)flat $S$-posets}, journal = {Categories and General Algebraic Structures with Applications}, volume = {8}, number = {1}, pages = {35-49}, year = {2018}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {10.29252/cgasa.8.1.35}, abstract = {In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are weakly po-flat.}, keywords = {Torsion free,po-torsion free,principally weakly flat,pomonoid,$S$-poset}, url = {https://cgasa.sbu.ac.ir/article_44578.html}, eprint = {https://cgasa.sbu.ac.ir/article_44578_81b18d36c9840fe2d5160c1baf42be5a.pdf} }