In this paper, we introduce and study the q-Krull dimension of a commutative ring via its q-operation. A new characterization of τq-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 τq-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 \ ring, positively answers an question proposed by H. Kim.
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Xiaolei Zhang (2024) studied this question.
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