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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

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