Weakly torsion free S-posets
Xingliang Liang, Valdis Laan, Yanfeng Luo, Roghaieh Khosravi · Communications in Algebra · 2016
Bulman-Fleming et al. [1] introduced the properties flatness, (principal) weak flatness and torsion freeness of S-posets over pomonoids S, and presented the implication: “principal weak flatness ⇒ torsion freeness”. Golchin et al. [3] described flatness, weak flatness and principal weak flatness of right S-posets AS over a pomonoid S in terms of pullback preservation by the tensor multiplication functor AS⊗−. In this note we first show, by giving a counterexample, that this implication of Bulman-Fleming et al. is incorrect. Afterwards we provide examples that deny these descriptions of Golchin et al. In view of the above, we finally study another property of S-posets (we call it weak torsion freeness), which is weaker than principal weak flatness, and characterize pomonoids by this property.