On Gorenstein projective, injective and flat dimensions: a functorial description with applications

Lars Winther Christensen; Anders Juel Frankild; Henrik Granau Holm

On Gorenstein projective, injective and flat dimensions: a functorial description with applications

Lars Winther Christensen, Anders Juel Frankild, Henrik Granau Holm

240 Citations (Scopus)

595 Downloads (Pure)

Abstract

Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings.
As opposed to their classical counterparts, these dimensions do not immediately come with practical and robust criteria for finiteness, not even over commutative noetherian local rings. In this paper we enlarge the class of rings known to admit good criteria for finiteness of Gorenstein dimensions:

Original language	English
Journal	Journal of Algebra
Volume	302
Issue number	1
Pages (from-to)	231-279
ISSN	0021-8693
Publication status	Published - 2006

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AU - Christensen, Lars Winther

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AB - Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical counterparts, these dimensions do not immediately come with practical and robust criteria for finiteness, not even over commutative noetherian local rings. In this paper we enlarge the class of rings known to admit good criteria for finiteness of Gorenstein dimensions:

M3 - Journal article

SN - 0021-8693

VL - 302

SP - 231

EP - 279

JO - Journal of Algebra

JF - Journal of Algebra

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