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

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.