C-χ-内射模、C-χ-平坦模和χ-凝聚环  

C-χ-injective Modules,C-χ-flat Modules andχ-coherent Rings

作　　者：李星宇 赵仁育 LI Xingyu;ZHAO Renyu(College of Mathematics and Statistics,Northwest Normal University,Lanzhou,Gansu,730070,P.R.China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《数学进展》2024年第6期1217-1226,共10页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.11861055,12061061)。

摘　　要：设S,R是环,_(S)C_(R)是半对偶双模,χ是一些有限表示右R-模的类.本文引入了C-χ-内射模和C-χ-平坦模的概念,研究了这两类模的一些性质,证明了R是χ-凝聚环当且仅当C-χ-平坦模的直积是C-χ-平坦的,当且仅当C-χ-内射模的正向极限是C-χ-内射的,当且仅当对任意右S-模M,M的C-χ-内射性与其示性模的C-χ-平坦性等价,当且仅当每个左S-模都有C-χ-平坦预包络,也当且仅当每个右S-模都有C-χ-内射覆盖,并且C-χ-内射模的纯子模是C-χ-内射的.本文统一推广了一些已知结果,并自然地产生了一些新的结论.Let S,R be rings,_(S)C_(R)a semidualizing bimodule andχa class of some finitely presented right R-modules.The notions of C-χ-injective modules and C-χ-flat modules are introduced.Some properties of these two classes of modules are studied,and it is shown that R isχ-coherent if and only if any direct product of C-χ-flat modules is C-χ-flat,if and only if any direct limit of C-χ-injective modules is C-χ-injective,if and only if for any right S-module M,the C-χ-injectivity of M coincides with the C-χ-flatness of the character module of M,if and only if every left S-module has a C-χ-flat preenvelope,if and only if every right S-module has a C-χ-injective cover and every pure submodule of a C-χ-injective module is C-χ-injective.Some known results are unified and some new cases are naturally generated.

关 键 词：半对偶模 χ-凝聚环 C-χ-内射模 C-χ-平坦模 

分 类 号：O153.3[理学—数学]