精确的结构和纯度

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-07-11 DOI:10.1016/j.aim.2025.110433

Kevin Schlegel

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引用次数: 0

摘要

我们把带产品的局部有限呈现范畴的纯粹性理论与有限呈现对象的完整子范畴上的精确结构的研究联系起来。在纯度上下文中的性质被转化为关于精确结构的性质。我们专门讨论了一个Artin代数上的模范畴，证明了一般模与特定的极大精确结构是一一对应的。

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Exact structures and purity

We relate the theory of purity of a locally finitely presented category with products to the study of exact structures on the full subcategory of finitely presented objects. Properties in the context of purity are translated to properties about exact structures. We specialize to the case of a module category over an Artin algebra and show that generic modules are in one to one correspondence with particular maximal exact structures.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.