Gorenstein homological dimensions

By Henrik Holm. 2004

842 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/42e194b45097618b78b73c3b4f42e76e3109d158

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In Algebra and Number Theory

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Rings Over Which the Class of Gorenstein Flat Modules is Closed Under Extensions (2008, methodology): “2. Every ring with finite weak dimension is left GF-closed. Proof. 1. Follows by [ 10, Theorem 3.7 ].”
Monic representations and Gorenstein-projective modules (2011, background): “and the fact that GP(A) is closed under extensions and the kernels of epimorphisms; see, for example, [Holm 2004].”
Semi-dualizing modules and related Gorenstein homological dimensions (2004, background): “A C ] 2 7 M ay We show how each such module gives rise to three new homological dimensions which we call C–Gorenstein projective, C–Gorenstein injective, and C–Gorenstein flat dimension, and investigate the properties of these dimensions.”
Generalized Tate cohomology (2005, background): “Since proj $ dimKer\beta<\infty$ , we have $Ext_{R}^{1}(L,Ker\beta)=0$ ([5], Proposition 2.”
Homotopy Equivalences induced by Balanced Pairs (2008, background): “acyclic and for any projective module Q the Hom complex HomR(P •, Q ) is acyclic (also see [19,22]).”
G-dimension over local homomorphisms. Applications to the Frobenius endomorphism (2003, result): “ step constitutes the bulk of work in this section and builds on recent work of Christensen, Frankild, and Holm [14]. They have informed us that they can prove the same result by using the methods in [22]. Step 3. The last step consists of verifying that when G-dimϕ(X) is ﬁnite, it is sandwiched bet”
Gorenstein dimension and proper actions (2009, background): “In [14] the following characterization of finite Gorenstein projective dimension is given.”
Proper Resolutions and Gorenstein Categories (2012, background): “Gorenstein projective and injective modules and some related generalized versions have been studied by many authors, see [1,4,6–8,10–21], and the literatures listed in them.”
Ascent Properties of Auslander Categories (2005, neutral): “See [16, 19, 32] for details on Gorenstein dimensions.”