Let A be a finite-dimensional algebra over an algebraically closed field k,ε the category of all exact sequences in A-rood, Mp （respectively, Ml） the full subcategory of C consisting of those objects with projecti...Let A be a finite-dimensional algebra over an algebraically closed field k,ε the category of all exact sequences in A-rood, Mp （respectively, Ml） the full subcategory of C consisting of those objects with projective （respectively, injective） middle terms. It is proved that Mp （respectively, MI） is contravariantly finite （respectively, covariantly finite） in ε. As an application, it is shown that Mp = MI is functorially finite and has Auslander-Reiten sequences provided A is selfinjective. Keywords category of exact sequences, contravariantly finite subcategory, functorially finite subcategory Auslander-Reiten sequences, selfinjective algebra展开更多
基金supported by National Natural Science Foundation of China(Grant No.11271257)National Science Foundation of Shanghai Municiple(Granted No.13ZR1422500)
文摘Let A be a finite-dimensional algebra over an algebraically closed field k,ε the category of all exact sequences in A-rood, Mp （respectively, Ml） the full subcategory of C consisting of those objects with projective （respectively, injective） middle terms. It is proved that Mp （respectively, MI） is contravariantly finite （respectively, covariantly finite） in ε. As an application, it is shown that Mp = MI is functorially finite and has Auslander-Reiten sequences provided A is selfinjective. Keywords category of exact sequences, contravariantly finite subcategory, functorially finite subcategory Auslander-Reiten sequences, selfinjective algebra
