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

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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: It now includes, for instance, the rings encountered in commutative algebraic geometry and, in the non-commutative realm, $k$--algebras with a dualizing complex.
Sections 2 and 3 reorganized; added proofs of Lemmas (2.4) and (5.6); added Theorem (5.10). 42 pp. To appear in J. Algebra

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Commutative Algebra, Rings and Algebras, 13D05, 13D07, 13D45, 16E05, 16E10, 16E30, 18E30, 18G10, 18G20, 18G35, 18G40

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http://salesiana.dossiersoluciones.com/handle/123456789/99965

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403156
 http://arxiv.org/abs/math/0403156

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arXiv