两类环上模的Gorenstein投射性、内射性与平坦性  

Gorenstein Projective and Gorenstein Injective Properties of Modules on Special Rings

作　　者：李艳午[1] 袁力 陈倩倩 LI Yanwu;YUAN Li;CHEN Qianqian(Department of Basic Education,Wuhu Institute of Technology,Wuhu 241003,Anhui,China)

机构地区：[1]芜湖职业技术学院基础教学部,安徽芜湖241003

出　　处：《山西师范大学学报（自然科学版）》2023年第4期9-14,共6页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：安徽省教育厅2020年自然科学研究重点项目(KJ2020A0916)。

摘　　要：研究了两类环上模的Gorenstein投射性、内射性与平坦性.首先,通过环上每个单模具有本质的平坦包络,得到环上模的Gorenstein投射性与内射性的刻画.然后,以凝聚环为中介,研究了满足一定条件下环上模的几种平坦性.The Gorenstein projective,injective and flatness of modules over two types of rings are studied.First of all,through the Gorenstein projective and injective characterizations of modules over a ring are obtained.Then,some flatness properties of modules over rings under certain conditions are studied by using condensed rings as mediators.

关 键 词：Gorenstein投射性 Gorenstein内射性 平坦性 QF-环 凝聚环 平坦包络 

分 类 号：O153.3[理学—数学]