Monoform objects and localization theory in abelian categories

IF 0.5 4区数学 Journal of Homotopy and Related Structures Pub Date : 2017-09-06 DOI:10.1007/s40062-017-0188-9

Reza Sazeedeh

引用次数: 6

Abstract

Let \({\mathcal {A}}\) be an abelian category. In this paper we study monoform objects and atoms introduced by Kanda. We classify full subcategories of \({\mathcal {A}}\) by means of subclasses of \({\mathrm{ASpec}}{\mathcal {A}}\), the atom spectrum of \({\mathcal {A}}\). We also study the atomical decomposition and localization theory in terms of atoms. As some applications of our results, we study the category Mod-A where A is a fully right bounded noetherian ring.

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阿贝尔范畴的单形对象与局部化理论

设\({\mathcal {A}}\)是一个阿贝尔范畴。本文研究了神田引入的单形体和原子。我们用\({\mathrm{ASpec}}{\mathcal {A}}\)的子类，\({\mathcal {A}}\)的原子谱来划分\({\mathcal {A}}\)的完整的子类。我们还从原子的角度研究了原子分解和局部化理论。作为我们结果的一些应用，我们研究了范畴Mod-A，其中A是一个完全右有界诺瑟环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

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