Categories of exact sequences with projective middle terms

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 c...

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Bibliographic Details
Published inScience China. Mathematics Vol. 57; no. 3; pp. 477 - 482
Main Authors Song, KeYan, Zhang, YueHui
Format Journal Article
LanguageEnglish
Published Heidelberg Science China Press 01.03.2014
Subjects
Algebra
Applications of Mathematics
Categories
China
Mathematical analysis
Mathematics
Mathematics and Statistics
Sequences
代数闭域
全相
分类
反变有限子范畴
射影
序列
有限维代数
熔点
contravariantly finite subcategory
functorially finite subcategory
18G05
category of exact sequences
selfinjective algebra
18B05
Auslander-Reiten sequences
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Summary: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
Bibliography:category of exact sequences, contravariantly finite subcategory, functorially finite subcategory,Auslander-Reiten sequences, selfinjective algebra
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
11-1787/N
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ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-013-4760-4