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Some examples of noncommutative local rings

  • D. A. Jordan (a1)

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In this paper we construct examples which answer three questions in the general area of noncommutative Noetherian local rings and rings of finite global dimension. The examples are formed in the same basic way, beginning with a commutative polynomial ring A over a field k and a k-derivation δ of A, taking the skew polynomial ring R = A[x;δ] and localizing at a prime ideal of the form IR, where I is a prime ideal of A invariant under δ. The localization is possible by a result of Sigurdsson [13].

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References

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1.Bell, A. D. and Sigurdsson, G., Catenarity and Gelfand-Kirillov dimension in Ore extensions, preprint (University of Southern California-Northern Illinois University).
2.Brown, K. A., Hajarnavis, C. R. and MacEacharn, A. B., Noetherian rings of finite global dimension, Proc. London Math. Soc. 44 (1982), 349371.
3.Chatters, A. W. and Jordan, D. A., Non-commutative unique factorization rings, J. London Math. Soc. (2) 33 (1986), 2232.
4.Cohn, P. M., Non-commutative unique factorisation domains, Trans Amer. Math. Soc. 109 (1963), 313331.
5.Hajarnavis, C. R. and Williams, S., Maximal orders in Artinian rings, J. Algebra 90 (1984), 375–384.
6.Jordan, D. A., Noetherian Ore extensions and Jacobson rings, J. London Math. Soc. (2) 10 (1975), 281291.
7.Jordan, D. A., Primitive Ore extensions, Glasgow Math. J. 18 (1977), 9397.
8.Kaplansky, I., Commutative rings, revised edition (University of Chicago Press, 1974).
9.Maury, G., Nouveaux exemples d'ordres maximaux, Comm. Algebra 14 (1986), 15151517.
10.Maury, G. and Raynaud, J., Ordres maximaux au sens de K. Asano, Lecture Notes in Mathematics 808 (Springer, 1980).
11.McConnell, J. C. and Robson, J. C., Noncommutative Noetherian rings, (Wiley, 1988).
12.Müller, B. J., Localization in non-commutative Noetherian rings, Canad. J. Math. 28 (1976), 600610.
13.Sigurdsson, G., Links between prime ideals in differential operator rings, J. Algebra 102 (1986), 260283.
14.Walker, R., Local rings and normalizing sets of elements, Proc. London Math. Soc. (3) 24 (1972), 2745.

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Some examples of noncommutative local rings

  • D. A. Jordan (a1)

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