l-分解与l-维数  

l-resolutions and l-dimensions

作　　者：曾月迪 林丽芳 ZENG Yue-di;LIN Li-fang(Department of Mathematics and Finance,Putian College,Putian 351100,China)

机构地区：[1]莆田学院数学与金融学院,福建莆田351100

出　　处：《数学的实践与认识》2020年第18期167-173,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61772292);福建省自然科学基金(2018J01426);福建省高校杰出青年人才培育计划。

摘　　要：设R是一个有单位元的结合环,l是包含所有内射左R-模的左R-模类,则M是l-内射(约化l-内射)的当且仅当M是一个左R-模l-预覆盖(l-覆盖)E→l的核,且E是内射的.当环R关于l-预覆盖核是可经内射分解的,刻画了左l-分解、左l-维数和导出函子之间的关系,并给出应用.let R be an associative ring with identity,and l be a class of left R-modules which contains all injective left R-modules.A left R-module M is l-injective(reduced linjective)if and only if M is a kernel of E→L which is a l-precover(l-cover)of a left R-module l with E injective.If R is a ring that kernels of l-precovers factor through injective modules,the relations of left l-resolution,left l-dimension and derived fuctors are charecterized,and some applications are given.

关 键 词：l-内射 左l-维数 左l-分解 约化 预覆盖 

分 类 号：O153.3[理学—数学]