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A classification of some thick subcategories in locally noetherian Grothendieck categories

Part of: Abelian categories Homological algebra

Published online by Cambridge University Press:  23 November 2023

Kaili Wu  and
Xinchao Ma
Kaili Wu*
Affiliation:
College of Science, Nanjing Forestry University, Nanjing, 210037, China
Xinchao Ma
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China
*
Corresponding author: Kaili Wu; Email: kailywu@163.com
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Abstract

Let $\mathcal{A}$ be a locally noetherian Grothendieck category. We classify all full subcategories of $\mathcal{A}$ which are thick and closed under taking arbitrary direct sums and injective envelopes by injective spectrum. This result gives a generalization from the commutative noetherian ring to the locally noetherian Grothendieck category.

Keywords

locally noetherian Grothendieck categoriesthick subcategoriesinjective envelopes

MSC classification

Primary: 18E10: Exact categories, abelian categories
Secondary: 18G05: Projectives and injectives
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 66 , Issue 1 , January 2024 , pp. 175 - 182
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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