Homological dimensions of unbounded complexes

doi:10.1016/0022-4049(91)90144-Q

Journal of Pure and Applied Algebra

Volume 71, Issues 2–3, 31 May 1991, Pages 129-155

Dedicated to Hideyuki Matsumura on his sixtieth birthday

https://doi.org/10.1016/0022-4049(91)90144-Q Get rights and content

Under an Elsevier user license

open archive

Abstract

This paper explores various notions of projective, injective, and flat dimensions, arising from recent constructions of resolutions of unbounded complexes, proposed by N. Spaltenstein and by S. Halperin with the authors. The different versions of each dimension are compared to each other, and also to the classical concepts, whenever these may be defined. Cohomological characterizations of the dimensions are provided in terms of vanishing of appropriate derived functors. The behavior of the dimensions under change of rings is investigated.

Cited by (0)

^∗: Supported by the Danish Research Academy, the University of Copenhagen, and the University of Nice. Current address: Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA.

^∗∗: Supported by the Danish Research Council.