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arXiv · 2404.09429

$q$-Krull dimension of commutative rings

Xiaolei Zhang
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Abstract

In this paper, we introduce and study the $q$-Krull dimension of a commutative ring via its $q$-operation. A new characterization of $\tau_q$-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 $\tau_q$-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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Xiaolei Zhang. 2024-04-15. $q$-Krull dimension of commutative rings. https://arxiv.org/abs/2404.09429

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