On F-Almost Split Sequences  

作　　者：Xiao Jin ZHANG Zhao Yong HUANG 

机构地区：[1]College of Mathematics & Physics, Nanjing University of Information Science & Technology, Nanjing 210044, P. R. China [2]Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第6期1149-1164,共16页数学学报（英文版）

基　　金：Partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060284002);National Natural Science Foundation of China (Grant No. 10771095);National Natural Science Foundation of Jiangsu Province of China (Grant No. BK2007517)

摘　　要：Let A be an Artinian algebra and F an additive subbifunctor of Ext,（-, -） having enough projectives and injectives. We prove that the dualizing subvarieties of mod A closed under F-extensions have F-almost split sequences. Let T be an F-cotilting module in mod A and S a cotilting module over F = End（T）. Then Horn（-, T） induces a duality between F-almost split sequences in ⊥FT and almost sl31it sequences in ⊥S, where addrS = Hom∧（f（F）, T）. Let A be an F-Gorenstein algebra, T a strong F-cotilting module and 0→A→B→C→0 and F-almost split sequence in ⊥FT.If the injective dimension of S as a Г-module is equal to d, then C≌（ΩCM^-dΩ^dDTrA^＊）^＊,where（-）^＊=Hom（g,T）.In addition, if the F-injective dimension of A is equal to d, then A≌ΩMF^-dDΩFop^-d TrC≌ΩCMF^-d ≌F^d DTrC.Let A be an Artinian algebra and F an additive subbifunctor of Ext,（-, -） having enough projectives and injectives. We prove that the dualizing subvarieties of mod A closed under F-extensions have F-almost split sequences. Let T be an F-cotilting module in mod A and S a cotilting module over F = End（T）. Then Horn（-, T） induces a duality between F-almost split sequences in ⊥FT and almost sl31it sequences in ⊥S, where addrS = Hom∧（f（F）, T）. Let A be an F-Gorenstein algebra, T a strong F-cotilting module and 0→A→B→C→0 and F-almost split sequence in ⊥FT.If the injective dimension of S as a Г-module is equal to d, then C≌（ΩCM^-dΩ^dDTrA^＊）^＊,where（-）^＊=Hom（g,T）.In addition, if the F-injective dimension of A is equal to d, then A≌ΩMF^-dDΩFop^-d TrC≌ΩCMF^-d ≌F^d DTrC.

关 键 词：F-almost split sequences almost split sequences F-Gorenstein algebras 

分 类 号：O157.5[理学—数学] O153.3[理学—基础数学]