Let
R be a Noetherian prime ring with an automorphism σ and a left σ-derivation δ, and let
X be an invertible ideal of
R with σ(
X) =
X. We define an Ore-Rees ring
S =
R[
Xt; σ, δ] which is a subring of an Ore extension
R[
t; σ, δ], where
t is an indeterminate. It is shown that if
R is a maximal order, then so is
S. In case σ = 1, we define the concepts of (δ;
X)-stable ideals of
R and of (δ;
X)-maximal orders and prove that
S is a maximal order if and only if
R is a (δ;
X)-maximal order. Furthermore we give a complete description of v-
S-ideals, which is used to characterize
S to be a generalized Asano ring. In case δ = 0, we define the concepts of (σ;
X)-invariant ideals of
R and of (σ;
X)-maximal orders in order to show that
S is a maximal order if and only if
R is a (σ;
X)-maximal order. We also give examples
R such that either
R is a (δ;
X)-maximal order or is a (σ;
X)-maximal order but they are not maximal orders.
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