Cohen-Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras

By Apostolos Beligiannis. 2005

165 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/eedc682296ba075867de426e2ed594f7ff198e86

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Citations in the corpus

On Artin Algebras Arising from Morita Contexts (2013, background): “sting of the ﬁnitely generated Gorenstein-projective Λ-modules. It is well known, see [11, Proposition 3.10], that when Λ is Gorenstein then GprojΛ = {X | Extn Λ(X,Λ) = 0, ∀n≥ 1}. Finally recall from [11], [12] that an Artin algebra Λ is said to be of ﬁnite Cohen-Macaulay type if the category GprojΛ”
Gorenstein Homological Algebra of Artin Algebras (2017, background): “ceptions the results in this report are contained in the existing literature. This report may be viewed as a preparation for reading the beautiful theory of virtually Gorenstein algebras developed in [15, 12, 13, 14]. 3 Chapter 2 Preliminaries 2.1 Gorenstein-Projective Modules Inthis section we stud”
Algebras with radical square zero are either self-injective or CM-free (2011, background): “Gorenstein projective modules projective? Here, for the notion of arbitrary Gorenstein projective module, we refer to [12] and [4].”
Monic representations and Gorenstein-projective modules (2011, background): “ules ([AB], where it was called a module of G-dimension zero); it become an important ingredient in the relative homologicalalgebra ([EJ]) and in the representation theory of algebras (see e.g. [AR], [B], [GZ], [IKM]); and plays a central role in the Tate cohomology of algebras (see e.g. [AM] and [B”
The Gorenstein-projective modules over a monomial algebra (2015, background): “ and extensions; compare [1, (3.11)]. THE GORENSTEIN-PROJECTIVE MODULES OVER A MONOMIAL ALGEBRA 3 The Gorenstein-projective modules are also called Cohen-Macaulay modules in the literature. Following [3], an algebra Ais CM-ﬁnite provided that up to isomorphism there are only ﬁnitely many indecomposa”
On algebras of finite Cohen-Macaulay type (2011, methodology): “if Λ is of inﬁnite CM-type. Finally by using that the stable triangulated category GprojΛ of ﬁnitely generated Gorenstein projective modules over a virtually Gorenstein algebra Λ admits Serre duality [26] and recent results of Amiot [1] and Keller-Reiten [49, 50], we give descriptions of GprojΛ, in ”
Relative singularity categories and Gorenstein‐projective modules (2007, methodology): “Theorem 6.7 and [ 7 ], Theorem 6.6), and Iyengar-Krause ([15], Theorem 5.4 (2)) using different”