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Prime ideals in skew and $q$-skew polynomial rings

About this Title

K. R. Goodearl and E. S. Letzter

Publication: Memoirs of the American Mathematical Society
Publication Year: 1994; Volume 109, Number 521
ISBNs: 978-0-8218-2583-9 (print); 978-1-4704-0098-9 (online)
DOI: https://doi.org/10.1090/memo/0521
MathSciNet review: 1197519
MSC: Primary 16S36; Secondary 16S30, 16S32, 16U20

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Table of Contents

Chapters

  • 1. Introduction
  • 2. Preliminaries for $S$ = $R$[$y; \tau , \delta$]
  • 3. Tau-delta-prime coefficient rings
  • 4. Each prime ideal of $S$ is associated to a unique $\tau$-orbit in spec$R$
  • 5. Annihilator primes and induced bimodules
  • 6. Prime ideals in quadratic (-1)-skew extensions
  • 7. Prime ideals in $S$ associated to infinite orbits. The general case
  • 8. Prime ideals in $S$ associated to infinite orbits. The $q$-skew case
  • 9. Prime ideals in $S$ associated to finite orbits. The general case
  • 10. Prime ideals in $S$ associated to finite orbits. The $q$-skew case
  • 11. Classification of prime ideals in $q$-skew extensions
  • 12. Irreducible finite dimensional representations of $q$-skew extensions
  • 13. Quantized Weyl algebras
  • 14. Prime factors of coordinate rings of quantum matrices
  • 15. Chains of prime ideals in iterated Ore extensions