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Height one prime ideals of certain iterated skew polynomial rings

Published online by Cambridge University Press:  24 October 2008

David A. Jordan
David A. Jordan
Affiliation:
Department of Pure Mathematics, University of Sheffield, The Hicks Building, P.O. Box 597, Sheffield S10 2UN
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Extract

(1·1) Introduction. This paper is concerned with the prime and primitive ideals of certain iterated skew polynomial rings in two variables. These rings include those constructed in [7] but an extra parameter, ρ, has been introduced to the construction. This leads to greater variety in the behaviour of the height one prime ideals.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 3 , November 1993 , pp. 407 - 425
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

REFERENCES

[1]Chatters, A. W.. Non-commutative unique factorisation domains. Math. Proc. Cambridge Philos. Soc. 95 (1984), 49–54.CrossRefGoogle Scholar
[2]Chatters, A. W. and Jordan, D. A.. Non-commutative unique factorisation rings. J. London Math. Soc. (2) 33 (1986), 22–32.CrossRefGoogle Scholar
[3]Cohn, P. M.. Free Rings and their Relations, 2nd edn (Academic Press, 1985).Google Scholar
[4]Goldie, A. W. and Michler, G. O.. Ore extensions and polycyclic group rings. J. London Math. Soc. (2) 9 (1974), 337–345.CrossRefGoogle Scholar
[5]Goodearl, K. R.. Prime ideals in skew polynomial rings and quantized Weyl algebras. J. Algebra 150 (1992), 324–377.CrossRefGoogle Scholar
[6]Jordan, D. A.. Primitive skew Laurent polynomial rings. Glasgow Math. J. 19 (1978), 79–85.CrossRefGoogle Scholar
[7]Jordan, D. A.. Iterated skew polynomial rings and quantum groups. J. Algebra 156 (1993), 194–218.CrossRefGoogle Scholar
[8]Jordan, D. A.. Krull and global dimension of certain iterated skew polynomial rings. Abelian Groups and Noncommutative Rings, a Collection of Papers in Memory of Robert B. Warfield, Jr., Contemporary Mathematics. Amer. Math. Soc. 130 (1992), 201–213.Google Scholar
[9]Jordan, D. A.. Primitivity in skew Laurent polynomial rings and related rings. Math. Z., to appear.Google Scholar
[10]Jordan, D. A.. Finite-dimensional simple modules over certain iterated skew polynomial rings, preprint, University of Sheffield.Google Scholar
[11]Kaplansky, I.. Fields and Rings (Univ. of Chicago Press, 1969).Google Scholar
[12]McConnell, J. C. and Robson, J. C.. Noncommutative Noetherian Rings (Wiley, 1987).Google Scholar
[13]Seidenberg, A.. Derivations and integral closure. Pacific J. Math. 16 (1966), 167–173.CrossRefGoogle Scholar
[14]Woronowicz, S. L.. Twisted SU(2)-group. An example of a non-commutative differential calculus. Publ. R.M.I.S., Kyoto Univ. 23 (1987), 117–181.Google Scholar
[15]Zariski, O. and Samuel, P.. Commutative Algebra, vol. I (Van Nostrand, Princeton, 1958).Google Scholar