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Local cohomology and Foxby classes
Let R be a commutative Noetherian ring and I a proper ideal of R . In this paper, we study finitely generated R -modules M with only one non-vanishing...
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Gorenstein Rings via Homological Dimensions, and Symmetry in Vanishing of Ext and Tate Cohomology
The aim of this article is to consider the spectral sequences induced by tensor-hom adjunction, and provide a number of new results. Let R be a...
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Another version of cosupport in D(R)
The goal of the article is to develop a theory dual to that of support in the derived category D( R ). This is done by introducing ‘big’ and ‘small’...
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A Study of Tate Homology via the Approximation Theory with Applications to the Depth Formula
In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part of the paper we generalize a result of Avramov and...
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On a Generalized Auslander-Reiten Conjecture
It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric Auslander condition (SAC) are equivalent, and (GARC)...
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Auslander-Reiten Conjecture in a Dual Vein
We consider a dual notion of the famous Auslander-Reiten Conjecture in case of Noetherian algebras over commutative Noetherian rings. Firstly, in the...
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On Modules M such that both M and M∗ are Semi-Gorenstein-Projective
Let A be an artin algebra. An A -module M is semi-Gorenstein-projective provided that Ext i ( M , A ) = 0 for all i ≥ 1. If M is Gorenstein-projective, then...
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On Modules with Reducible Complexity
In this paper we generalize a result, concerning a depth equality over local rings, proved independently by Araya and Yoshino, and Iyengar. Our...
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Generalized Tilting Modules Over Ring Extension
Let Γ be a ring extension of R . We show the left Γ-module U = Γ Ⓧ r C with the endmorphism ring End Γ U = Δ is a generalized tilting module when R C is a...
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Strict Mittag-Leffler conditions and locally split morphisms
In this paper, we prove that any pure submodule of a strict Mittag-Leffler module is a locally split submodule. As applications, we discuss some...
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A Generalized Dade’s Lemma for Local Rings
We prove a generalized Dade’s Lemma for quotients of local rings by ideals generated by regular sequences. That is, given a pair of finitely...
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Structure of Irreducible Homomorphisms to/from Free Modules
The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated...
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Gorenstein Injective Filtrations Over Cohen-Macaulay Rings with Dualizing Modules
Over a noetherian ring, it is a classic result of Matlis that injective modules admit direct sum decompositions into injective hulls of quotients by...
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Vanishing of stable homology with respect to a semidualizing module
We investigate stable homology of modules over a commutative noetherian ring R with respect to a semidualzing module C , and give some vanishing...
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Relative Cohomology and Generalized Tate Cohomology
We compare relative cohomology theories arising from using different proper resolutions of modules. Criteria for the vanishing of such distinctions...
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Vanishing of Tate homology — An application of stable homology for complexes
It has been proved that the vanishing of Tate homology is a sufficient condition for the derived depth formula to hold in [ J. Pure Appl. Algebra , 219 ,...
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V-Gorenstein injective modules preenvelopes and related dimension
Let R and S be associative rings and S V R a semidualizing ( S - R )-bimodule. An R -module N is said to be V -Gorenstein injective if there exists a Hom ...