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Fonction de Hilbert-Samuel dans les anneaux locaux réguliers non-commutatifs

Published online by Cambridge University Press:  18 May 2009

J. Alev
J. Alev
Affiliation:
Université De Paris, VI 4 Place Jussieu 75230 Paris Cedex 05, France
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En algèbre non-commutative, on dit qu'un anneau noethérien A est local si:

(i) le radical de Jacobson M de A est un idéal maximal,

(ii) ∩ Mn = (0),

(iii) A/M est artinien simple.

Dans [9], Walker definit un anneau local régulier comme un anneau local A dont le radical de Jacobson M est engendré par une A-suite centralisante x1; x2, …, xt, [4], et demontre alors que:

t = cldim A = Kdim A = rgldim A = pdAA/M.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 24 , Issue 1 , January 1983 , pp. 65 - 69
Copyright
Copyright © Glasgow Mathematical Journal Trust 1983

References

Références

1.Alev, J., Polynôme de Hilbert-Samuel dans les algèbres enveloppantes et les algèbres de groupe, Israel J. Math. 37 (1980), 231–240.Google Scholar
2.Bohro, W. and Kraft, H., Über die Gelfand-Kirillov-Dimension, Math. Ann. 220 (1976), 1–24.Google Scholar
3.Nouazé, Y. et Gabriel, P., Idéaux premiers de l'algèbre enveloppante d'une algèbre de Lie nilpotente, J. Algebra 6 (1967), 77–99.CrossRefGoogle Scholar
4.McConnell, J. C., The intersection theorem for a class of non-commutative rings, Proc. London Math. Soc. (3) 17 (1967), 487–498.Google Scholar
5.Pickel, P. F., Rational cohomology of nilpotent groups and Lie algebras, Comm. Algebra 6 (1978), 409–419.CrossRefGoogle Scholar
6.Roseblade, J. E., Applications of the Artin-Rees lemma to group rings, Symposia Mathematica, Vol. XVII (Academic Press, 1976), 471–478.Google Scholar
7.Smith, P. F., On non-commutative regular local rings, Glasgow Math. J. 17 (1976), 98–102.CrossRefGoogle Scholar
8.Stafford, J. T. and Wallach, N. R., The restriction of admissible modules to parabolic subalgebras, à paraître.Google Scholar
9.Walker, R., Local rings and normalizing sets of elements, Proc. London Math. Soc. (3) 24 (1972), 27–45.CrossRefGoogle Scholar
10.Zariski, O. et Samuel, P., Commutative Algebra II, (Van Nostrand, 1960).CrossRefGoogle Scholar