具有有限整体Gorenstein维数的环

任伟, 张瑜

doi:10.13371/j.cnki.chin.q.j.m.2017.03.004

数学季刊 >

2017 , Vol. 32 >Issue 3: 255 - 260

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.03.004

具有有限整体Gorenstein维数的环

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Department of Mathematics, Northwest Normal University

REN Wei(1983-), male, native of Longnan, Gansu, an associate professor of Northwest Normal University, Ph.D., engages in homological algebra; ZHANG Yu(1994-), female, native of Yuncheng, Shanxi, a master degree candidate of Northwest Normal University, engages in homological algebra.

收稿日期: 2015-12-11

网络出版日期: 2020-10-22

基金资助

Supported by the National Natural Science Foundation of China(11401476)； Supported by the Project for Universities of Gansu Province(2015A-019)；

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On Rings with Finite Global Gorenstein Dimensions

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Department of Mathematics, Northwest Normal University

Received date: 2015-12-11

Online published: 2020-10-22

Supported by

Supported by the National Natural Science Foundation of China(11401476)； Supported by the Project for Universities of Gansu Province(2015A-019)；

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摘要

As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou’s equality of global Gorenstein dimension is given.

关键词： generalized Gorenstein ring; Gorenstein projective(injective) dimension

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任伟, 张瑜 . 具有有限整体Gorenstein维数的环[J]. 数学季刊, 2017 , 32(3) : 255 -260 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.03.004

Abstract

Key words： generalized Gorenstein ring; Gorenstein projective(injective) dimension

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