  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.
