Roghaieh Khosravi - Department of Mathematics, Fasa University, Fasa, P.O. Box ۷۴۶۱۷- ۸۱۱۸۹, Iran
Xingliang Liang - Department of mathematics, Shaanxi University of Science and Technology, Shaanxi, P.O. Box ۷۱۰۰۲۱, 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 ۳.۲۲ 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.

Torsion free, po-torsion free, principally weakly flat, pomonoid, S-poset