by John C. Baez
Publisher: University of California 2001
Number of pages: 56
The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.
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by W. B. Vasantha Kandasamy - American Research Press
This is the first book on the Smarandache algebraic structures that have two binary operations. Semirings are algebraic structures with two binary operations enjoying several properties and it is the most generalized structure.
by George M. Bergman - Henry Helson
From the contents: Free groups; Ordered sets, induction, and the Axiom of Choice; Lattices, closure operators, and Galois connections; Categories and functors; Universal constructions in category-theoretic terms; Varieties of algebras; etc.
by W. B. Vasantha Kandasamy, Florentin Smarandache - Educational Publisher
This book brings out how sets in algebraic structures can be used to construct the most generalized algebraic structures, like set linear algebra / vector space, set ideals in groups and rings and semigroups, and topological set vector spaces.
by Claude Chevalley - The Mathematical Society Of Japan
This is the reproduction of the beautiful lectures delivered by Professor C. Chevalley at the University of Tokyo in April-June 1954. Contents: Graded algebras; Tensor algebras; Clifford algebras; Some applications of exterior algebras.