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$q$-Krull dimension of commutative rings (2404.09429v1)

Published 15 Apr 2024 in math.AC

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.