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III - Alternative algebras

Published online by Cambridge University Press:  07 November 2024

Skip Garibaldi ,
Holger P. Petersson  and
Michel L. Racine
Skip Garibaldi
Affiliation:
Institute for Defense Analyses, USA
Holger P. Petersson
Affiliation:
FernUniversität in Hagen
Michel L. Racine
Affiliation:
University of Ottawa
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Summary

This chapter is devoted to a short excursion into the theory of alternative algebras over commutative rings. We prove Artin’s theorem, according to which alternative algebras on two generators are associative. We study in detail McCrimmon’s theory of homotopes, which plays a strong role in this book and therefore merits greater emphasis here than one might find in other discussions of alternative algebras.

Keywords

alternative algebraMoufang identityinvertibilityArtin’s theoremisotope
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Chapter
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Albert Algebras over Commutative Rings
The Last Frontier of Jordan Systems
 , pp. 109 - 122
Publisher: Cambridge University Press
Print publication year: 2024

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