持久化模块的平面外壳和注入壳

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI:10.1016/j.jpaa.2025.107874

Eero Hyry, Ville Puuska

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引用次数: 0

摘要

基于拓扑数据分析的最新进展，我们建立了持久化模块的注入壳和平面盖之间的Matlis对偶关系。这扩展到最小平面分辨率和最小内射分辨率之间的对偶性。我们利用了Enochs和Xu提出的平扭模和平盖理论。通过这个理论，我们可以处理非驯服的、甚至是点向有限维的持久性模块。

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Flat covers and injective hulls of persistence modules

Motivated by recent progress in topological data analysis, we establish a Matlis duality between injective hulls and flat covers of persistence modules. This extends to a duality between minimal flat and minimal injective resolutions. We utilize the theory of flat cotorsion modules and flat covers developed by Enochs and Xu. By means of this theory we can work with persistence modules which are not tame or even pointwise finite-dimensional.

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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.