Memoirs of the American Mathematical Society 1994; 106 pp; softcover Volume: 109 ISBN10: 0821825836 ISBN13: 9780821825839 List Price: US$38 Individual Members: US$22.80 Institutional Members: US$30.40 Order Code: MEMO/109/521
 There has been continued interest in skew polynomial rings and related constructions since Ore's initial studies in the 1930s. New examples not covered by previous analyses have arisen in the current study of quantum groups. The aim of this work is to introduce and develop new techniques for understanding the prime ideals in skew polynomial rings \(S=R[y;\tau , \delta ]\), for automorphisms \(\tau\) and \(\tau\)derivations \(\delta\) of a noetherian coefficient ring \(R\). Goodearl and Letzter give particular emphasis to the use of recently developed techniques from the theory of noncommutative noetherian rings. When \(R\) is an algebra over a field \(k\) on which \(\tau\) and \(\delta\) act trivially, a complete description of the prime ideals of \(S\) is given under the additional assumption that \(\tau ^{1}\delta \tau = q\delta\) for some nonzero \(q\in k\). This last hypothesis is an abstraction of behavior found in many quantum algebras, including \(q\)Weyl algebras and coordinate rings of quantum matrices, and specific examples along these lines are considered in detail. Readership Research mathematicians. Table of Contents  Introduction
 Preliminaries for \(S=R[y;\tau ,\delta ]\)
 Taudeltaprime coefficient rings
 Each prime ideal of \(S\) is associated to a unique \(\tau\)orbit in \(\operatorname{spec}R\)
 Annihilator primes and induced bimodules
 Prime ideals in quadratic \((1)\)skew extensions
 Prime ideals in \(S\) associated to infinite orbits. The general case
 Prime ideals in \(S\) associated to infinite orbits. The \(q\)skew case
 Prime ideals in \(S\) associated to finite orbits. The general case
 Prime ideals in \(S\) associated to finite orbits. The \(q\)skew case
 Classification of prime ideals in \(q\)skew extensions
 Irreducible finite dimensional representations of \(q\)skew extensions
 Quantized Weyl algebras
 Prime factors of coordinate rings of quantum matrices
 Chains of prime ideals in iterated Ore extensions
 References
