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Published online by Cambridge University Press: 07 November 2024
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.
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