阿贝尔范畴中的扭转简单对象

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2024-10-09 DOI:10.1016/j.jpaa.2024.107818

Sergio Pavon

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引用次数: 0

摘要

我们介绍了无阶梯范畴中扭转简单对象的概念：这些对象对于任何扭转对来说总是要么有扭转要么无扭转的。我们提出了一些有关其性质的一般结果，然后在不同的背景下研究了这一概念，例如阿尔金代数或交换诺特环上的模块范畴，以及投影线上的准相干剪切范畴。

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Torsion-simple objects in abelian categories

We introduce the notion of torsion-simple objects in an abelian category: these are the objects which are always either torsion or torsion-free with respect to any torsion pair. We present some general results concerning their properties, and then proceed to investigate the notion in various contexts, such as the category of modules over an artin algebra or a commutative noetherian ring, and the category of quasi-coherent sheaves over the projective line.

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.