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II - Foundations

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 starts out with a short introduction to the language of nonassociative algebras over commutative rings. It then proceeds to familiarize the reader with two of the most important elementary techniques utilized in this book: scalar extensions (also known as base change) and finitely generated projective modules. Standard properties of involutions and quadratic maps are also recalled before we conclude the chapter with a short introduction into Roby’s theory (1963) of polynomial laws.

Keywords

Nonassociative algebradivision algebrabase changelocalizationprojective moduleinvolutionquadratic spaceLG ringpolynomial law
Type
Chapter
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Albert Algebras over Commutative Rings
The Last Frontier of Jordan Systems
 , pp. 43 - 108
Publisher: Cambridge University Press
Print publication year: 2024

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