Classification of Simple Modules of the Ore Extension $$K[X][Y; f\frac{d}{dX}]$$

Abstract

For the algebras in the title of the paper, a classification of simple modules is given, an explicit description of the prime and completely prime spectra is obtained, the global and the Krull dimensions of are computed. Keywords A skew polynomial ring • A prime ideal • A completely prime ideal • A simple module • The global dimension • The Krull dimension • A normal element

Identities for a parametric Weyl algebra over a ring

“…Then Lopes and Solotar [20] described the Hochschild cohomology HH • (A h ) over a field of arbitrary characteristic. Over an algebraically closed field of zero characteristic simple A h -modules were independently classified by Bavula [5]. In recent preprints [6], [7] Bavula continued the study of the automorphism group of A h .…”