%0 Journal Article %T On (po-)torsion free and principally weakly (po-)flat $S$-posets %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Khosravi, Roghaieh %A Liang, Xingliang %D 2018 %\ 01/01/2018 %V 8 %N 1 %P 35-49 %! On (po-)torsion free and principally weakly (po-)flat $S$-posets %K Torsion free %K po-torsion free %K principally weakly flat %K pomonoid %K $S$-poset %R 10.29252/cgasa.8.1.35 %X 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. %U https://cgasa.sbu.ac.ir/article_44578_81b18d36c9840fe2d5160c1baf42be5a.pdf