N -ary algebras

Source abstract

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.