Semi-stability and topologies on R-Sp
Semi-stability and topologies on R-Sp
复制标题
R-Sp 上的半稳定性和拓扑
DOI：
10.1080/00927877608822139
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发表时间：
1976
影响因子：
0.7
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.在[4]中，J. Golan引入了半稳定扭转理论的概念。一个挠理论称为半稳定的，如果每个不可分解的内射R-模F要么是7-挠的，要么是7-挠自由的。这是稳定挠理论的推广，它具有所有7-挠左R-模的局部化子范畴在取内射包络下闭的性质。（Gabriel [2].）这两个概念在左诺特环上的挠理论中是一致的。本文刻画了挠理论的半稳定性，推广了作者161号论文的结果，并应用这些结果研究了半稳定环R-sp上的拓扑，即每个挠理论都是半稳定的环。
1. Introduction. Let R be a ring with unit element. In [4] J. Golan has introduced the notion of semi-stable torsion theory. A torsion theory 7 i, s called semi-stable if, every indecomposable injective R-module F is either 7-torsion or 7-torsion free. This is the generalization of the stable torsion theory, which has the property that the localizing subcategory of all 7-torsion left R-modules is closed under taking inj ective envelopes.(Gabriel [2].) The two notions coincide for torsion theories over left noetherian rings. In this note we characterize the semi-stability of torsion theories, extending the results of the author's paper 161, and apply the results to study the topologies on R-sp for semi-stable rings, ie rings for which every torsion theory is semi-stable.