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Superassociative systems with given semigroup of inner right translations

Published online by Cambridge University Press:  14 November 2011

H. Länger
H. Länger
Affiliation:
Technische Universität Wien, Institut für Algebra und Mathematische Strukturtheorie, Argentinierstraße 8, A-1040 Wien
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Synopsis

Let n be some fixed positive integer and let (A, f) be some fixed algebra of type n + 1. (A, f) is called an n-dimensional superassociative system if f(f(x0,…, xn), ȳ) = f(x0, f(x1, ȳ), …, f(xn, ȳ)) for any x0, …, xn ∈ A and for any ȳ ∈ An. The semigroup ({f(., ā) | ā ∈ An},∘) is called the semigroup of inner right translations of (A, f). In the present note a theorem is derived in order to determine all n-dimensional superassociative systems with a given semigroup of inner right translations. As an example, using this method all two-element superassociative systems are determined.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 3-4 , 1981 , pp. 247 - 249
Copyright
Copyright © Royal Society of Edinburgh 1981

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