Mathematics – Commutative Algebra
Scientific paper
2004-03-09
Mathematics
Commutative Algebra
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
Scientific paper
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.
Christensen Lars Winther
Frankild Anders
Holm Henrik
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