学术报告
On the flatness of S-acts and S-posets - 梁星亮博士（陕西科技大学）
题目：On the flatness of S-acts and S-posets
报告人：梁星亮博士（陕西科技大学）
摘要：In S-acts (S-posets) as a representation of a monoid(pomonoid) S have a close relationship with homological algebra. In this talk, two main problems will be discussed. On the one hand, we first define Condition (PF)" in the category of S-acts, which lies strictly between weak pullback flatness and Condition (P') and prove that Condition(PF)" coincides with the conjunction of Conditions (P') and (E'). Furthermore, we give a classification of monoids by Condition (PF)" of (cyclic, Rees factor) acts. On the other hand, Bulman-Fleming et al. presented in 2006 the implication: “principal weak flatness => torsion freeness”. Afterwards Golchin et al. described flatness, weak flatness and principal weak flatness of right S-posets over a pomonoid S in terms of pullback preservation by the tensor multiplication functor. By giving some counterexamples, we show that this implication of Bulman-Fleming et al. is incorrect, and 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).
时间：11月17日（周五） 14:00-15:00
地点：首师大校本部新教二楼727
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