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- Title
On Proper and Exact Relative Homological Dimensions.
- Authors
Bennis, Driss; García Rozas, J.R.; Mao, Lixin; Oyonarte, Luis
- Abstract
In Enochs' relative homological dimension theory occur the (co)resolvent and (co)proper dimensions, which are defined by proper and coproper resolutions constructed by precovers and preenvelopes, respectively. Recently, some authors have been interested in relative homological dimensions defined by just exact sequences. In this paper, we contribute to the investigation of these relative homological dimensions. First we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint pairs. Then relative global dimensions are studied, which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories. At the end of this paper, relative derived functors are studied and generalizations of some known results of balance for relative homology are established.
- Subjects
DIMENSION theory (Algebra)
- Publication
Algebra Colloquium, 2020, Vol 27, Issue 3, p621
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386720000516