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N-ary algebras

Published online by Cambridge University Press:  22 January 2016

Renate Carlsson
Renate Carlsson*
Affiliation:
Mathematisches Seminar Universität HamburgBundesstraβe 55 2Hamburg 13
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N-ary algebras are modules with a n-fold multiplication which we assume to be associative if nothing else is stated. They are a canonical generalization of binary and ternary associative algebras. Ternary rings were first investigated by Lister [8]. The aim of this note is to show that the Wedderburn structure theory and the usual cohomology for binary associative algebras can be extended to n-ary algebras. For ternary algebras this has been done in [8] and [1]. Moreover analogous results are wellknown for Lie and alternative triple systems, and for ternary Jordan pairs.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 78 , May 1980 , pp. 45 - 56
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[1] Carlsson, R., Cohomology of associative triple systems, Proc. Amer. Math. Soc, 60 (1976), 1–7.CrossRefGoogle Scholar
[2] Carlsson, R., Der Wedderburnsche Hauptsatz für alternative Tripelsysteme und Paare, Math. Ann., 228 (1977), 233–248.CrossRefGoogle Scholar
[3] Harris, B., Cohomology of Lie triple systems and Lie-algebras with involution, Trans. Amer. Math. Soc, 98 (1961), 148–162.CrossRefGoogle Scholar
[4] Herstein, I. N., Noncommutative rings, The Mathematical Association of America, Carus Mathematical Monograph, no. 15, sec. pr. 1971.Google Scholar
[5] Jacobson, N., Structure of rings, rev. ed. Amer. Math. Soc. Colloqu. Publ., vol. 37, Amer. Math. Soc, Providence R. I. 1964, repr. 1968.Google Scholar
[6] Jacobson, N., Lie-algebras, Interscience Tracts in Pure and Appl. Math., no. 10, Interscience, New York and London, 1962.Google Scholar
[7] Kurosh, A. G., Multioperator rings and algebras, Russian Math. Surveys, 24 (1969), 1–13.CrossRefGoogle Scholar
[8] Lister, W. G., Ternary rings, Trans. Amer. Math. Soc, 154 (1971), 37–55.CrossRefGoogle Scholar
[9] McCrimmon, K., A characterization of the Jacobson-Smiley radical, J. Algebra, 18 (1971), 565–573.CrossRefGoogle Scholar
[10] Meyer, F. de and Ingraham, E., Separable algebras over commutative rings, Springer, Lecture note, 181 (1971).Google Scholar
[11] Röhrl, H., Algebras and differential equations, Nagoya Math. J., 68 (1977), 59–122.CrossRefGoogle Scholar
[12] Taft, E. J., Cleft algebras with operator groups, Portugal. Math., 20 (1961), 195–198.Google Scholar