On Proper and Exact Relative Homological Dimensions

• 作者: Driss Bennis J.R.García Rozas Lixin Mao Luis Oyonarte
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 621-642
• 页数: 22页
• 语种: 英文
• DOI: 10.1142/S1005386720000516

摘要

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.