q-Krull dimension of commutative rings

2024/04/15 by Xiaolei Zhang, Zhang, Xiaolei
Mathematics · Neuroscience · #Axon Guidance and Neuronal Signaling #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2404.09429

openalex publication_date 2024/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce and study the q-Krull dimension of a commutative ring via its q-operation. A new characterization of τ_q-von Neumann regular rings is obtained, and some properties of rings q-Krull dimension 0 are studied. Moreover, we characterize the q-Krull dimension of τ_q-Noetherian rings in terms of Krull dimension of some total quotient rings. Besides, we show that every ring with w-Krull dimension 0 is a \DW ring, positively answers an question proposed by H. Kim.

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