We study primality, hypercentrality, simplicity, and localization and the second layer condition in skew enveloping algebras and iterated differential operator rings. We give sufficient conditions for the skew enveloping algebra of a nilpotent Lie algebra with coefficient ring containing the rational numbers to be a simple ring, and we give necessary and sufficient conditions in the case that the Lie algebra is Abelian. Our main results show that if $L$ is a finite dimensional solvable Lie algebra and $R$ is an Artinian ring or a commutative Noetherian algebra over $k$, then the skew enveloping algebra $R\#U(L)$ satisfies the second layer condition. We discuss consequences of this for localization and use the localization theory to state a classical Krull dimension versus global dimension inequality when $k$ is uncountable.
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