弱Gorenstein分次模

宋彦辉; 郭婷

doi:10.13568/j.cnki.651094.651316.2024.01.30.0001

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弱Gorenstein分次模

更新时间：2026-01-21

- 弱Gorenstein分次模
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 41, Issue 5, Pages: 556-561(2024)
- 作者机构：
  
  兰州信息科技学院通识教育学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2024.01.30.0001
  CLC： O153.3
- Published：2024
- 稿件说明：
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[1]宋彦辉,郭婷.弱Gorenstein分次模[J].新疆大学学报(自然科学版中英文),2024,41(05):556-561.
[1]宋彦辉,郭婷.弱Gorenstein分次模[J].新疆大学学报(自然科学版中英文),2024,41(05):556-561. DOI： 10.13568/j.cnki.651094.651316.2024.01.30.0001.

DOI：10.13568/j.cnki.651094.651316.2024.01.30.0001.

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.

Abstract

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 modules 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.

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Keywords

references

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