An Introduction to Nonassociative Algebras (Dover Books on Mathematics: Volume 22)

By: Richard D. Schafer

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Synopsis: "An important addition to the mathematical literature … contains very interesting results not available in other books; written in a plain and clear style, it reads very smoothly." — Bulletin of the American Mathematical SocietyThis concise study was the first book to bring together material on the theory of nonassociative algebras, which had previously been scattered throughout the literature. It emphasizes algebras that are, for the most part, finite-dimensional over a field. Written as an introduction for graduate students and other mathematicians meeting the subject for the first time, the treatment's prerequisites include an acquaintance with the fundamentals of abstract and linear algebra.After an introductory chapter, the book explores arbitrary nonassociative algebras and alternative algebras. Subsequent chapters concentrate on Jordan algebras and power-associative algebras. Throughout, an effort has been made to present the basic ideas, techniques, and flavor of what happens when the associative law is not assumed. Many of the proofs are given in complete detail.