分次绝对clean模和分次level模  

Graded absolutely clean modules and graded level modules

作　　者：狄振兴 狄蓉蓉 DI Zhen-xin;DI Rong-rong(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院

出　　处：《西北师范大学学报（自然科学版）》2019年第6期28-32,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11971388)

摘　　要：在任意分次环R上引入了分次绝对clean模和分次level模的概念,证明了(gr-FI∞,gr-F∞)和(gr-F∞,gr-FI∞)构成了分次R-模范畴中具有某种特殊性质的对偶对,其中gr-FI∞为由所有分次绝对clean模构成的子范畴,gr-F∞为由所有分次level模构成的子范畴.作为应用,证明了任意分次左R-模都有分次绝对clean覆盖和分次level预包络.The concepts of graded absolutely clean modules and graded level modules over a graded ring R are intruduced,and it is proved that in the category of all graded R-modules,the pairs(gr-F∞,gr-FI∞)and(gr-F∞,gr-FI∞)form two duality pairs with some special properties,where gr-FI∞(resp.,gr-F∞)denotes the subcategory of all graded absolutely clean R-modules(resp.,graded level R-modules).As applications,it is proved that any graded left R-module has a graded absolutely clean cover and a graded level preenvelope.

关 键 词：FP∞型分次模 分次绝对clean模 分次level模 覆盖 预包络 

分 类 号：O153.3[理学—数学]