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Modular Jordan nilalgebras

Published online by Cambridge University Press:  20 January 2009

Jose Angel Anquela
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, C/Calvo Sotelo S/N, 33007 Oviedo, Spain
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Abstract

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In this paper we give a classification up to isomorphism of Jordan nilalgebras whose lattices of subalgebras are modular when the ground field is algebraically closed.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Amayo, R. K. and Schwarz, J., Modularity in Lie algebras, Hiroshima Math. J. 10 (1980), 311322.CrossRefGoogle Scholar
2.Anquela, J. A., Modular nilpotent Jordan algebras, in Proceedings of the Workshop on Nonassociative Algebraic Models, held at Universidad de Zaragoza, Zaragoza, Spain, April 1989 (Edited by Santos González and Hyo Chul Myung, Nova Science Publishers, Inc. New York 1992), 1724.Google Scholar
3.Anquela, J. A., On modular Jordan algebras, in the Proceedings of the Fifth International Conference in Hadronic Mechanics and Non Potential Interactions (University of Northern Iowa, August 1990, Noya Science Publishers, Inc.), to appear.Google Scholar
4.Elduque, A. C., On semimodular Mal'cev algebras, Arch. Math. 50 (1988), 328336.CrossRefGoogle Scholar
5.Elduque, A. C., A note on modularity in Mal'cev algebras, Arch. Math. 50 (1988), 424428.CrossRefGoogle Scholar
6.Grätzer, G., General lattice theory (Mathematische Reihe, Band 52, Birkhäuser Verlag Basel und Stuttgart 1978).CrossRefGoogle Scholar
7.Jacobson, N., Structure and representations of Jordan algebras. (Amer. Math. Soc. Colloquium Publications 39, A.M.S. Providence, Rhode Island 1968).Google Scholar
8.Kolman, B., Semimodular Lie algebras, J. Sci. Hiroshima Univ. Ser. 29 (1965), 149163.Google Scholar
9.Zhevlakov, K. A., Slinko, A. M., Shestakov, I. P. and Shirshov, A. I., Rings that are nearly associative (Pure and Applied Mathematics. Academic Press, New York, 1982).Google Scholar