  In this paper we describe the prime ideals of some important classes of skew
PBW extensions, using the classical technique of extending and contracting
ideals. Skew PBW extensions include as particular examples Weyl algebras,
enveloping algebras of finite-dimensional Lie algebras (and its quantization),
Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum
matrices, among many others.
