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Polynomial rings over rings integral over their centres

Published online by Cambridge University Press:  17 April 2009

C. L. Wangneo
C. L. Wangneo
Affiliation:
Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201.
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Abstract

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We prove in this paper that every finitely generated critical module over A[X] is compressible where A is a Noetherian ring integral over a subring of its centre. Here A[X] denotes the polynomial ring over A in a commuting indeterminate X.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 1 , August 1986 , pp. 11 - 23
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Amitsur, A.S., “Algebras over infinite fields”, Proc. Amer. Math. Soc., 7 (1956), 35–48.CrossRefGoogle Scholar
[2]Blair, W.D., “Right Noetherian rings integral over their centers”, J. Algebra, 27 (1973), 187–198.Google Scholar
[3]Chamarie, M. and Hudry, A., “Anneaux Noetherians A Droit Entries sur Sous-Anneau de Leur Center”, Comm. Algebra, (2) 6 (1978), 203–222.CrossRefGoogle Scholar
[4]Goldie, A.W., “the structure of prime rings under ascending chain condition”, Proc. London Math. Soc., (3) 8 (1958), 589–608.CrossRefGoogle Scholar
[5]Goldie, A.W., “A survey of progress in noncommutative Noetherian rings” Ring Theory, Proc. 1978 Antwerp Conf., Lect. Notes Pure Appl. Math., 51 91979), 61–79.Google Scholar
[6]Gordon, R. and Robson, J. C., “Krull dimension”, Mem. Amer. Math. Soc., 133 (1971).Google Scholar
[7]Gordon, R., “Some aspects of non-commutative Noetherian rings. Lect. Notes in Math., 545 (1975).Google Scholar
[8]Goodearl, K. R. and Lenagan, T. H., “Krull dimension of differential operator rings 111: Non commutative coefficients”, Trans. Amer. Math. Soc., 275 (1983), 833–859.Google Scholar
[9]Jategaonker, A.V., “Jacobson's conjecture and modules over fully bounded Noetherian rings”, J. Algebra, (1) 30 (1974), 103–121.Google Scholar
[10]Lambek, J. and Michler, G., “The torsion theory at a prime ideal of a right Noetherain ring”, J. Algebra, (2) 25 (1973), 364–389.CrossRefGoogle Scholar
[11]Mueller, B.J., “Localization in non-commutative Noetherian rings”, Canad. J. Math., 28 (1976), 600–610.Google Scholar
[12]Small, L.W., “Orders in Artinian rings”, J. Algebra, 4 (1966), 13–41.CrossRefGoogle Scholar
[13]Stafford, J.T., “On the regular elements of Noetherian rings” Ring Theory, Proc. 1978 Antwerp Conf., Lect. Notes Pure Appl. Math., 51 (1979), 257–277.Google Scholar
[14]Wangneo, C.L. and Tewari, K., “Right Noetherian rings integral over their centers”, Comm. Algebra, (15) 7 (1979), 1573–1598.CrossRefGoogle Scholar