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Trivial Maximal 1-Orthogonal Subcategories For Auslander\s 1-Gorenstein Algebras
Huang Zhaoyong * #,Zhang Xiaojin
Department of Mathematics, Nanjing University
*Correspondence author
#Submitted by
Subject: Ring Theory
Funding: 国家自然科学基金,教育部博士点基金,江苏省自然科学基金(No.10771095,20060284002,BK2007517)
Opened online: 5 June 2009
Accepted by: none
Citation: Huang Zhaoyong ,Zhang Xiaojin .Trivial Maximal 1-Orthogonal Subcategories For Auslander\s 1-Gorenstein Algebras[OL]. [ 5 June 2009] http://www.paper.edu.cn/lwzx/en_releasepaper/content/32883
Let Λ be an Auslander\s 1-Gorenstein Artinian algebra with global dimension two. If Λ admits a trivial maximal 1-orthogonal subcategory of mod Λ, then for any indecomposable module M in mod Λ, we have that the projective dimension of M is equal to one if and only if so is its injective dimension and that M is injective if the projective dimension of M is equal to two. In this case, we further get that Λ is a tilted algebra.
Keywords:trivial maximal 1-orthogonal subcategories;Auslander\s 1-Gorenstein algebras;tilted algebras;indecomposable modules;projective dimension;injective dimension
论文给出了包含平凡的极大1-正交子范畴并且整体为数为2的Auslander’s 1-Gorenstein代数的结构(此类代数为倾斜代数)与同调性质,证明了一些列有理论意义的结果。论文推理正确,英语写作规范,论文中出现的一下笔误需要修改:1. P_7的交换图少了3个向下的箭头。2. P-9, -2行,Lemma 3.2(2)应该是Lemma 3.3(2)。 

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