Chain conditions for rings with enough idempotents with applications to category graded rings
type: Item
instance of: scholarly article
title: Chain conditions for rings with enough idempotents with applications to category graded rings
DOI: 10.1080/00927872.2024.2317459
author: Patrik Lundström
published in: Communications in Algebra
publication date: 2024-06-25T00:00:00Z
review text: Let \(S\) be a ring with enough idempotents, and let \({e_i}_{i\in I }\) be a complete set of idempotents for \(S\). The author proves that if \(S\) is left/right artinian (noetherian), then \(I\) is finite, and for every \(i\in I\), the ring \(e_iSe_i\) is left/right artinian (noetherian); moreover, under an additional condition, the converse also holds. This result is applied to certain category graded rings.
reviewed by: Andrei Marcus
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16S35
Mathematics Subject Classification ID: 20N02
zbMATH DE Number: 7870863
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7870863