On Proper and Exact Relative Homological Dimensions  

作　　者：Driss Bennis J.R.Garcia Rozas Lixin Mao Luis Oyonarte 

机构地区：[1]CeReMAR Center,Faculty of Sciences B.P.1014 Mohammed V University in Rabat,Rabat,Morocco [2]Dcpartamento de Matematicas,Universidad de Almeria,Almena 04071,Spain [3]Department of Mathematics and Physics,Nanjing Institute of Technology Nanjing 211167,China [4]Departamento de Matematicas,Universidad de Almena,Almena 04071,Spain

出　　处：《Algebra Colloquium》2020年第3期621-642,共22页代数集刊（英文版）

基　　金：The second and fourth authors were partially supported by the grant MTM2014-54439-P from Ministerio de Economia y Competitividad;The third author was partially supported by NSFC(11771202).

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.

关 键 词：self-orthogonal subcategory resolvent dimension exact dimension relative homological dimension relative group(co)homology balanced pair 

分 类 号：O15[理学—数学]