分次绝对clean模和分次level模

Graded absolutely clean modules and graded level modules

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.