环扩张上M-相对投射模和M-相对内射模的性质  

The Properties of M-relative Projective Modules and M-relative Injective Modules on Ring Extensions

作　　者：邹智勇 郭述锋 ZOU Zhiyong;GUO Shufeng(College of Mathematics and Statistics,Guangxi Normal University,Guilin,Guangxi 541004,China;College of Science,Guilin University of Aerospace Technology,Guilin,Guangxi 541004,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541004 [2]桂林航天工业学院理学院,广西桂林541004

出　　处：《桂林航天工业学院学报》2025年第1期21-27,37,共8页Journal of Guilin University of Aerospace Technology

基　　金：广西自然科学基金项目“扩张的相对同调理论研究”(2022GXNSFAA035532);桂林航天工业学院博士基金项目“扩张的相对同调维数”(20180601-20200601)。

摘　　要：在任意的环扩张上给出了M-相对投射模和M-相对内射模的定义及其等价刻画,并探讨了它们的基本性质。特别证明了M-相对投射模关于直和及直和项封闭,M-相对内射模关于直积及直和项封闭;当M为相对内射模时,M-相对投射模关于相对扩张封闭;当M为相对投射模时,M-相对内射模关于相对扩张封闭。This paper introduces the definitions of M-relative projective modules and M-relative injective modules over arbitrary ring extensions,and subsequently studies their equivalent characterizations and fundamental properties.In particular,M-relative projective modules are closed under direct sums and direct summands,whereas M-relative injective modules are closed under direct products and direct summands.Moreover,we establish that when is a M-relatively injective module,M-relative projective modules are closed under relative extensions;and when M is a relatively projective module,M-relative injective modules are closed under relative extensions.

关 键 词：环扩张 R S-正合列 M-相对投射模 M-相对内射模 

分 类 号：O153.3[理学—数学]