弱Gorenstein分次模  

Weak Gorenstein Graded Modules

作　　者：宋彦辉 郭婷 SONG Yanhui;GUO Ting(School of General Education,Lanzhou University of Information Science and Technology,Lanzhou Gansu 730300,China)

机构地区：[1]兰州信息科技学院通识教育学院,甘肃兰州730300

出　　处：《新疆大学学报（自然科学版中英文）》2024年第5期556-561,共6页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：甘肃省高校教师创新基金“Gorenstein弱同调模及复形的研究”(2023B-387)。

摘　　要：设R是分次环,引入弱Gorenstein gr-投射,gr-内射和gr-平坦模,给出了弱Gorenstein gr-投射模的等价刻画.证明了在分次n-Gorenstein环上,弱Gorenstein gr-投射R-模是Gorenstein gr-投射的.同时,证明了如果任意分次内射R-模具有有限的分次平坦维数,那么M是弱Gorenstein gr-平坦R-模当且仅当M是Gorenstein gr-平坦模.Let R be a graded ring.The concepts of weak Gorenstein gr-projective modules,gr-injective modules and gr-flat modules are introduced,and some homological characterizations of weak Gorenstein gr-projective mod-ules are given.It is shown that a weak Gorenstein gr-projective module is a Gorenstein gr-projective R-module over a graded n-Gorenstein ring R.Moreover,it is proved that:if any graded injective R-module has a finite graded flat dimension,then a graded module M is weak Gorenstein gr-flat if and only if M is Gorenstein gr-flat.

关 键 词：分次投射模 弱Gorenstein gr-投射模 分次平坦维数 弱Gorenstein gr-平坦模 

分 类 号：O154.2[理学—数学]