The relationship between homological properties and representation theoretic realization of artin algebras
The relationship between homological properties and representation theoretic realization of artin algebras
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DOI：
10.1090/s0002-9947-04-03482-8
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发表时间：
2003-07
影响因子：
1.3
通讯作者：
O. Iyama
中科院分区：
文献类型：
--
作者：
O. Iyama
我们将研究Artin代数理论中完全不同的对象之间的关系，即整体维数为2的Auslander正则环，挠理论，β-范畴和几乎交换范畴。我们将应用我们的结果Auslander-Reiten箭的特征化问题。0.1在具有加法生成元M的Krull-Schmidt范畴C的等价类与半完全环的Morita等价类之间存在一个双射，它由C7 → C（M，M）给出，而对于半完全环的Morita生成投射模范畴pr，匡威由7→ pr给出.虽然双射本身是相当形式化的，但研究下面（A）-（D）的关系将是非常富有成果的。本文的研究对象是在代数为阿尔蒂n的假设下.
We will study the relationship of quite different object in the theory of artin algebras, namely Auslander-regular rings of global dimension two, torsion theories, �-categories and almost abelian categories. We will apply our results to characterization problems of Auslander-Reiten quivers. 0.1 There exists a bijection between equivalence classes of Krull-Schmidt categories C with additive generators M and Morita-equivalence classes of semiperfect rings , which is given by C 7→ C(M, M) and the converse is given by 7→ pr for the category pr of finitely generated projective -modules. Although th is bijection itself is rather formal, it will be very fruitful to study the relationship of (A)-(D) below. The object of this paper is to study it under the assumption that is an arti n algebra.