C O N T E N T S

1. Introduction 1

2. Preliminaries for S = R[y; ry6] 6

3. Tau-delta-prime coefficient rings 15

4. Each prime ideal ofS is associated to a unique r-orbit in specR.... 28

5. Annihilator primes and induced bimodules 32

6. Prime ideals in quadratic (-l)-skew extensions 43

7. Prime ideals in S associated to infinite orbits. The general case 46

8. Prime ideals in S associated to infinite orbits. The q-skew case 53

9. Prime ideals in S associated to finite orbits. The general case 60

10. Prime ideals in S associated to finite orbits. The q-skew case 64

11. Classification of prime ideals in q-skew extensions 75

12. Irreducible finite dimensional representations of q-skew extensions. .. 80

13. Quantized Weyl algebras 83

14. Prime factors of coordinate rings of quantum matrices 88

15. Chains of prime ideals in iterated Ore extensions 100

References 104

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