$q$-Krull dimension of commutative rings
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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 with $q$-Krull dimension 0 are studied. Moreover, we characterize the $q$-Krull dimension of $\tau_q$-Noetherian rings in terms of the Krull dimension of certain total quotient rings. Additionally, we show that every ring with $w$-Krull dimension $0$ is a \DW\ ring.
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 with $q$-Krull dimension 0 are studied. Moreover, we characterize the $q$-Krull dimension of $\tau_q$-Noetherian rings in terms of the Krull dimension of certain total quotient rings. Additionally, we show that every ring with $w$-Krull dimension $0$ is a \DW\ ring.