关于S-系的正合序列及平坦性  

On Exact Sequence and Flatness Properties of S-acts

作　　者：李焕云 王胜杰 LI Huanyun;WANG Shengjie(Department of Public Teaching, Xinlian College of Henan Normal University, Zhengzhou 450046, China)

机构地区：[1]河南师范大学新联学院公共教学部,河南郑州450046

出　　处：《河南教育学院学报（自然科学版）》2021年第4期10-17,39,共9页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：河南师范大学新联学院校级教学研究项目(JY190311)。

摘　　要：设S是幺半群,B→fA→gC和0→B→fA→gC→0分别表示准正合序列和Rees短正合序列。针对准正合序列利用拉回图系统地证明了在一定的条件下S-系的平坦性质可以从C传递到A上;同时考虑了近来新出现的平坦性,给出了准(Rees短)正合序列关于这些性质从B、C传递到A上的条件。Let S be a monoid,B→fA→gC和0→B→fA→gC→0 denote quasi-exact sequences and Rees short exact sequences of S-acts respectively.It proves that conditions under which flatness properties of acts C in the quasi-exact sequences can be transferred to A.At the same time,considering new extensive flatness properties of S-acts recently,it obtains the condition over which the new flatness properties of acts B and C in the quasi-exact sequences or Rees short exact sequences can be transferred to A.

关 键 词：准正合序列 Rees短正合序列 拉回图 平坦性 

分 类 号：O152[理学—数学]