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Effective computation of the Gelfand-Kirillov dimension*

Published online by Cambridge University Press:  20 January 2009

José L. Bueso
Affiliation:
Department of Algebra, University of Granada, 18071-Granada, Spain
F. J. Castro Jiménez
Affiliation:
Department of Algebra, University of Granada, 18071-Granada, Spain
Pascual Jara
Affiliation:
Department of Algebra, University of Sevilla, 41071-Sevilla, Spain
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Abstract

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In this note we propose an effective method based on the computation of a Gröbner basis of a left ideal to calculate the Gelfand-Kirillov dimension of modules.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1997

Footnotes

*

Research partially supported by the European Human Capital and Mobility project (CHRX-CT93-0091).

References

REFERENCES

1. Apel, J. and Lassner, W., An extension of Buchberger's algorithm and calculations in enveloping fields of Lie algebras, J. Symbolic Comput. 6 (1988), 361370.CrossRefGoogle Scholar
2. Buchberger, B., Ein algorithmisches Kriterium for die Lösbarkeit eines algebraischen Gleichungssystems, Aequationes Math. 4 (1970), 374383.CrossRefGoogle Scholar
3. Castro, F., Thèse de 3eme cycle, (Univ. Paris VII, Oct–1984).Google Scholar
4. Castro, F., Calculs effectifs pour les idéaux d'opérateurs differentiels in Géométrie Algébrique et applications (Travaux en Cours, 24, Hermann, Paris, 1987).Google Scholar
5. Cox, D., Little, J. and O'shea, D., Ideals, Varieties and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra (Springer-Verlag, 1992).Google Scholar
6. Duflo, M., Certain algèbres de type fini sont des algèbres de Jacobson, J. Algebra 27 (1973), 358365.CrossRefGoogle Scholar
7. Kolchin, E. R., Differential algebra and algebraic groups (Academic Press, 1973).Google Scholar
8. Krause, G. R., Lenagan, T. H., Growth of algebras and Gelfand-Kirillov dimension (Pitman, 1985).Google Scholar
9. Lejeune-Jalabert, M., Effectivité des calculs polynomiaux (Cours de D.E.A., Univ. Grenoble, 19841985).Google Scholar
10. Mcconnell, J. C., Robson, J. C., Noncommutative noetherian rings (Wiley, 1987).Google Scholar