On (po-)torsion free and principally weakly (po-)flat $S$-posets

Document Type : Research Paper


1 Department of Mathematics, Fasa University, Fasa, P.O. Box 74617- 81189, Iran

2 Department of mathematics, Shaanxi University of Science and Technology, Shaanxi, P.O. Box 710021, China



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.


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