On Gorenstein Projective, Injective and Flat Dimensions - A Functorial Description with Applications

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dc.creatorChristensen, L. Winther
dc.creatorFrankild, A.
dc.creatorHolm, H.
dc.date2004-03-09
dc.date2005-12-13
dc.date.accessioned2026-07-07T06:36:01Z
dc.date.available2026-07-07T06:36:01Z
dc.descriptionGorenstein 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: It now includes, for instance, the rings encountered in commutative algebraic geometry and, in the non-commutative realm, $k$--algebras with a dualizing complex.
dc.descriptionSections 2 and 3 reorganized; added proofs of Lemmas (2.4) and (5.6); added Theorem (5.10). 42 pp. To appear in J. Algebra
dc.identifierhttps://arxiv.org/abs/math/0403156
dc.identifierhttp://arxiv.org/abs/math/0403156
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99965
dc.subjectCommutative Algebra
dc.subjectRings and Algebras
dc.subject13D05, 13D07, 13D45, 16E05, 16E10, 16E30, 18E30, 18G10, 18G20, 18G35, 18G40
dc.titleOn Gorenstein Projective, Injective and Flat Dimensions - A Functorial Description with Applications
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