A topological characterization of stable rings
A topological characterization of stable rings
复制标题
稳定环的拓扑表征
DOI：
10.1007/bf01220400
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发表时间：
1977
影响因子：
0.6
通讯作者：
Z. Papp
中科院分区：
文献类型：
--
作者：
Z. Papp
1.导论.设R是具有单位元的环. R-mod是左R-模的范畴，Sp（R-rood）是R-rood的谱，是不可分解的内射左模的同构类的集合。Goldston和Mewborn在[2]中定义了当R是左Noether环时Sp（R-rood）的一个拓扑。本文的主要结果是通过空间Sp（R-rood）的Goldston-Mewborn拓扑的性质来刻画左诺特环类中的左稳定左诺特环。2.背景和注释。这里考虑的所有环R都有一个单位元，并且每个R-模都是酉左R-模。对于挠率理论中未解释的概念、结果、术语和符号，我们可以参考Golan的书[1]，下面我们只总结那些在我们的讨论中最重要的概念。E（M），通常，表示R-模M的内射包络。
1. Introduction. Let R be a ring with unit element. R-mod is the category of left R-modules and Sp (R-rood), the spectrum of R-rood, is the set of isomorphism classes of indecomposable injective left modules. In [2] Goldston and Mewborn have defined a topology for Sp (R-rood) in the case when R is a left noetherian ring. The main result of this paper is a characterization of the left stable, left noetherian rings within the class of left noetherian rings through a property of the Goldston-Mewborn topology of the space Sp (R-rood).2. Background and notations. All rings R considered here are supposed to have an identity element and each R-module is a unitary left R-module. For unexplained concepts, results, terminologies and notations on torsion theories we refer to the book [1] of Golan, and in the following we summarize only those concepts that are most essential in our discussion. E (M), as usual, denotes the injective envelope of the R-module M.