Gorenstein injective dimension and Tor-depth of modules

1999 ◽  
Vol 72 (2) ◽  
pp. 107-117 ◽  
Author(s):  
Edgar E. Enochs ◽  
Overtoun M.G. Jenda
Keyword(s):  
Injective Dimension ◽  
Gorenstein Injective Dimension ◽  
Gorenstein Injective

A Bass Formula for Gorenstein Injective Dimension

2007 ◽  
Vol 35 (6) ◽  
pp. 1882-1889 ◽  
Author(s):  
Leila Khatami ◽  
Siamak Yassemi
Keyword(s):  
Injective Dimension ◽  
Gorenstein Injective Dimension ◽  
Gorenstein Injective

Gorenstein homological dimensions and some duality results

2017 ◽  
Vol 10 (03) ◽  
pp. 1750048
Author(s):  
Fatemeh Mohammadi Aghjeh Mashhad
Keyword(s):  
Local Ring ◽  
Duality Theorem ◽  
Projective Dimension ◽  
Injective Dimension ◽  
Duality Results ◽  
Dualizing Complex ◽  
Matlis Duality ◽  
Homological Dimensions ◽  
Gorenstein Injective Dimension ◽  
Gorenstein Injective

Let [Formula: see text] be a local ring and [Formula: see text] denote the Matlis duality functor. Assume that [Formula: see text] possesses a normalized dualizing complex [Formula: see text] and [Formula: see text] and [Formula: see text] are two homologically bounded complexes of [Formula: see text]-modules with finitely generated homology modules. We will show that if G-dimension of [Formula: see text] and injective dimension of [Formula: see text] are finite, then [Formula: see text] Also, we prove that if Gorenstein injective dimension of [Formula: see text] and projective dimension of [Formula: see text] are finite, then [Formula: see text] These results provide some generalizations of Suzuki’s Duality Theorem and the Herzog–Zamani Duality Theorem.

scholarly journals Finiteness of Gorenstein injective dimension of modules

2009 ◽  
Vol 137 (07) ◽  
pp. 2201-2207 ◽  
Author(s):  
Leila Khatami ◽  
Massoud Tousi ◽  
Siamak Yassemi
Keyword(s):  
Injective Dimension ◽  
Gorenstein Injective Dimension ◽  
Gorenstein Injective

Gorenstein cohomology of N-complexes

2019 ◽  
Vol 19 (09) ◽  
pp. 2050174
Author(s):  
Bo Lu ◽  
Zhenxing Di
Keyword(s):  
Projective Dimension ◽  
Complex Case ◽  
Binomial Coefficients ◽  
Cohomology Groups ◽  
Injective Dimension ◽  
Relative Cohomology ◽  
Gorenstein Injective Dimension ◽  
Gorenstein Injective ◽  
Gaussian Binomial Coefficients

Let [Formula: see text] and [Formula: see text] be [Formula: see text]-complexes with [Formula: see text] an integer such that [Formula: see text] has finite Gorenstein projective dimension and [Formula: see text] has finite Gorenstein injective dimension. We define the [Formula: see text]th Gorenstein cohomology groups [Formula: see text] [Formula: see text] via a strict Gorenstein precover [Formula: see text] of [Formula: see text] and a strict Gorenstein preenvelope [Formula: see text] of [Formula: see text]. Using Gaussian binomial coefficients we show that there exists an isomorphism [Formula: see text] which extends the balance result of Liu [Relative cohomology of complexes. J. Algebra 502 (2018) 79–97] to the [Formula: see text]-complex case.

scholarly journals Dual of the Auslander-Bridger formula and GF-perfectness

2007 ◽  
Vol 101 (1) ◽  
pp. 5 ◽  
Author(s):  
Parviz Sahandi ◽  
Tirdad Sharif
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Krull Dimension ◽  
Local Cohomology Module ◽  
Injective Dimension ◽  
Gorenstein Dimension ◽  
Finite Module ◽  
Gorenstein Injective Dimension ◽  
Gorenstein Injective

Ext-finite modules were introduced and studied by Enochs and Jenda. We prove under some conditions that the depth of a local ring is equal to the sum of the Gorenstein injective dimension and Tor-depth of an Ext-finite module of finite Gorenstein injective dimension. Let $(R,\mathfrak m)$ be a local ring. We say that an $R$-module $M$ with $\dim_R M=n$ is a Grothendieck module if the $n$-th local cohomology module of $M$ with respect to $\mathfrak m$, $\mathrm{H}_{\mathfrak m}^n (M)$, is non-zero. We prove the Bass formula for this kind of modules of finite Gorenstein injective dimension and of maximal Krull dimension. These results are dual versions of the Auslander-Bridger formula for the Gorenstein dimension. We also introduce GF-perfect modules as an extension of quasi-perfect modules introduced by Foxby.

scholarly journals Gorenstein Injective Dimension and Cohen-Macaulayness

2020 ◽  
Vol 5 (2) ◽  
pp. 157-164
Author(s):  
Reza Sazeedeh ◽  
fatemeh Savoji ◽  
◽  
Keyword(s):  
Injective Dimension ◽  
Gorenstein Injective Dimension ◽  
Gorenstein Injective
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