l-分解与l-维数

l-resolutions and l-dimensions

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.