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- Title
A QUILLEN MODEL STRUCTURE APPROACH TO HOMOLOGICAL DIMENSIONS OF COMPLEXES.
- Authors
WEI, REN; LIU, ZHONGKUI
- Abstract
In this paper, we first give an alternative characterization of the derived functor Ext via the Quillen model structure on the category of complexes induced by a given cotorsion pair in the category of modules, then based on this, we consider homological dimensions of complexes related to . As applications, we extend Gorenstein projective dimension of homologically bounded below complexes (in the sense of Christensen and coauthors) to unbounded complexes whenever R is Gorenstein. Moreover, we extend Stenström's FP-injective dimension from modules to complexes, define FP-projective dimension for complexes, and characterize Noetherian and von Neumann regular rings by these dimensions.
- Subjects
MATHEMATICAL models; HOMOLOGY theory; DIMENSIONS; CATEGORIES (Mathematics); MODULES (Algebra); NOETHERIAN rings; VON Neumann regular rings
- Publication
Journal of Algebra & Its Applications, 2014, Vol 13, Issue 3, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498813501065