ABSTRACT
Let be an automorphism of a ring R and T be the skew Laurent polynomial over-ring
. The extension map
which takes a two-sided ideal I of R to
is injective on the sub-lattice of ideals J such that
. We find necessary and sufficient conditions for
to be surjective, and from these conditions deduce known results regarding
and the possible simplicity of T. The main result is extended to crossed products by free abelian groups.