Abstract:
A ring R is said to be ideal Krull-symmetric if for any ideal I of R, the right Krull dimension of I is equal to the left Krull dimension of I. Let now R be commutative Noetherian ring. In this paper we show that certain
Ore extensions of R are ideal Krull-symmetric. The rings that we deal with are:
$S_t(R)=R[x_1;\sigma_1][x_2;\sigma_2]\dots[x_t,\sigma_t]$, the iterated skew-polynomial ring, where each
$\sigma_i$ is an automorphism of $S_{i-1}(R)$
$L_t(R) = R[x_1, x_1^{-1}; \sigma_1][x_2, x_2^{-1};\sigma_2\dots[x_t,x_t^{-1};\sigma_t]$, the iterated skew-Laurent polynomial ring, where each $\sigma_i$ is an
automorphism of $L_{i-1}(R)$
$D_t(R) = R[x_1;\delta_1][x_2;\delta_{2}]\dots[x_t;\delta_t]$, the iterated differential polynomial ring, where each $\delta_i$ is a derivation of $D_{i-1}(R)$ such that each $\delta_i\mid R$ is a derivation of R and,
$A_t(R)$ is any of $S_t(R)$ or $L_t(R)$, where $\sigma_i\mid R$ is an automorphism of R.
With this we prove that $A_t(R)$ and $D_t(R)$ are ideal Krull-symmetric.
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