![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
ABSTRACT
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.
Acknowledgements
The authors would like to give many thanks to the anonymous referee for his invaluable comments and suggestions, to Professor Husheng Qiao for his very helpful suggestions for improving this article, and to School of Mathematics and Statistics, Lanzhou University for support with this research. We would also like to thank Professor V. Gould for her useful communications.