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Number theory --- Algebraic fields --- Algebraic numbers --- Algebraïsche velden --- Corps algébriques --- Fields [Algebraic ] --- Galois [Theorie de ] --- Galois [Theorie van ] --- Galois theory --- Homologie --- Homology theory --- Théorie de Galois --- Algebraic fields. --- Galois theory. --- Homology theory. --- Corps algébriques --- Théorie de Galois --- Nombres, Théorie des. --- Number theory. --- Cohomologie. --- Galois cohomology --- Cohomologie galoisienne. --- Nombres, Théories des --- Cohomologie --- Cohomologie galoisienne --- Nombres, Théorie des --- Nombres algébriques, Théorie des

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The 1963 Göttingen notes of T. A. Springer are well-known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra. In the group-theoretical part use is made of some results from the theory of linear algebraic groups. The book will be useful to mathematicians interested in octonion algebras and Albert algebras, or in exceptional groups. It is suitable for use in a graduate course in algebra.

Group theory --- Cayley numbers (Algebra) --- Jordan algebras. --- Alternative rings --- Linear algebraic groups. --- Cayley, Octaves de --- Jordan, Algèbres de --- Anneaux alternatifs --- Groupes linéaires algébriques --- Cayley numbers --- Jordan algebras --- Linear algebraic groups --- Alternative rings. --- Cayley numbers. --- Jordan, Algèbres de --- Groupes linéaires algébriques --- Commutative algebra. --- Commutative rings. --- Group theory. --- Commutative Rings and Algebras. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Rings (Algebra)