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On Malcev algebras in which all subideals are ideals

Published online by Cambridge University Press:  14 November 2011

Alberto Elduque
Alberto Elduque
Affiliation:
Departamento de Algebra, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain†
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Synopsis

Malcev algebras in which the relation of being an ideal is transitive are studied as well as those Malcev algebras in which every subalgebra satisfies that condition. These algebras are closely related to those in which right multiplication by any element is semisimple and they are used to determine Malcev algebras with a relatively complemented lattice of subalgebras.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 3-4 , 1985 , pp. 353 - 363
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

1.Carlsson, R.. On the exceptional central simple non-Lie Malcev algebras. Trans. Amer. Math. Soc. 244 (1978), 173–184.Google Scholar
2.Elduque, A.. Estructura de un álgebra de Malcev a través de su reticulo de subálgebras (Spanish). Doctoral Dissertation, Zaragoza 1984.Google Scholar
3.Farnsteiner, R.. On ad-semisimple Lie algebras. J. Algebra 83 (1983), 510–519.CrossRefGoogle Scholar
4.Filippov, V. T.. Semiprimary Mal'tsev algebras of characteristic 3. Algebra i Logika 14 (1975), 204–214.Google Scholar
5.Filippov, V. T.. Central simple Mal'tsev algebras. Algebra i Logika 15 (1976), 147–151.Google Scholar
6.Gein, A. G. and Muhin, J. N.. Complements to subalgebras of Lie algebras (Russian). Ural. Gos. Univ. Mat. Zap. 12 (1980), 24–48.Google Scholar
7.Gratzer, G.. General Lattice Theory (Stuttgart: Birkhäuser, 1978).Google Scholar
8.Jacobson, N.. Lie Algebras (New York: Interscience, 1962).Google Scholar
9.Kolman, B.. Relatively complemented Lie algebras. J. Sci. Hiroshima Univ. Ser. A-I 31 (1967), 1–11.Google Scholar
10.Kuzmin, E. N.. Mal'tsev algebras and their representations. Algebra i Logika 7 (1968), 48–69.Google Scholar
11.Kuzmin, E. N.. Simple Mal'tsev algebras over a field of characteristic zero. Dokl. Akad. Nauk USSR 181 (1968), 1324–1326.Google Scholar
12.Ribenboim, P. R.. Algebraic numbers (Pure and Applied Mathematics 27) (New York: Wiley-Interscience, 1972).Google Scholar
13.Sagle, A. A.. Malcev algebras. Trans. Amer. Math. Soc. 101 (1961), 426–458.CrossRefGoogle Scholar
14.Seligman, G.. Rational Methods in Lie Algebras (New York: Marcel Dekker, 1976).Google Scholar
15.Suzuki, M.. Structure of a Group and the Structure of its Lattice of Subgroups (Ergebnisse der Mathematik und ihrer Grenzgebiete) (Berlin: Springer, 1956).Google Scholar
16.Varea, V. R.. On Lie algebras in which the relation of being ideal is transitive. Comm. Algebra 13 (1985), 1135–1150.CrossRefGoogle Scholar