Structure of Algebras - (Dover Books on Mathematics) by A Adrian Albert (Paperback)

About the Book

Building a comprehensive foundational text in associative algebra theory, this seminal work innovates with advanced topics like crossed products, cyclic algebras, factorization of division algebras, representations, and involution algebras.

Book Synopsis

This seminal work offers a rigorous treatment of associative algebras, serving as a comprehensive foundational text. A. Adrian Albert pioneered methods for handling cyclic and crossed product algebras, developed novel factorization techniques for division algebras of prime-power degree, and unified algebraic results to yield simpler, generalized solutions that reduced reliance on complex classical ideal theory. The book also linked algebraic theory to new applications, such as Riemann matrices and involution algebras, thereby bridging historic algebraic theory with contemporary advances and applications in geometry and analysis. This once out-of-print masterpiece is now accessible to a new generation of students and includes a comprehensive bibliography of related topics for researchers.

From the Back Cover

A. Adrian Albert exposes the intricacies of linear associative algebras and mathematical structures in this comprehensive textbook. A preliminary discussion of algebraic fundamentals, including the Wedderburn structure theory, leads to the examination of commutator subalgebras, automorphisms, splitting fields, and index reduction factors. Building a solid foundation in crossed products, cyclic algebras, and normal division algebra factorization, Albert links algebraic representations to applications inspired by the Riemann matrix theory and the theory of involutorial simple algebras. Structure of Algebras features an exposition of historic algebraic theory with contemporary advances. Includes a comprehensive bibliography of related topics for researchers.