Weakly torsion free S-posets

摘要

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 double right arrow torsion freeness. Golchin et al. 3 described flatness, weak flatness and principal weak flatness of right S-posets A(S) over a pomonoid S in terms of pullback preservation by the tensor multiplication functor A(S)circle times-. 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.