The Extension Dimension of Subcategories and Recollements of Abelian Categories  

作　　者：Xin MA Ye Yang PENG Zhao Yong HUANG 

机构地区：[1]College of Science,Henan University of Engineering,Zhengzhou 451191,P.R.China [2]Department of Mathematics,Nanjing University,Nanjing 210093,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第4期1042-1058,共17页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.11971225,12171207,12001168);Henan University of Engineering(Grant Nos.DKJ2019010,XTYR-2021JZ001);the Key Research Project of Education Department of Henan Province(Grant No.21A110006)。

摘　　要：We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements.LetΛ',Λ,Λ"be art in algebras such that(modΛ',mod A,modΛ")is a recollement,and let D'and D"be subcategories of modΛand modΛ"respectively.For any n,m≥0,under some conditions,we get dimΩ^(k)(D)≤dimΩ^(n)(D')+dimΩ^(m)(D")+1,where k=max{m,n}and D is the subcategory of modΛglued by D'and D";moreover,we give a sufficient condition such that the converse inequality holds true.As applications,some results for Igusa-Todorov subcategories and syzygy finite sub categories are obtained.

关 键 词：Recollements extension dimension Igusa–Todorov subcategories syzygy finite subcategories 

分 类 号：O154.1[理学—数学]