Structure of Algebras (Dover Books on Mathematics) - Softcover

Albert, A. Adrian

Softcover

ISBN 10: 0486856372 ISBN 13: 9780486856377

Publisher: Dover Publications, 2026

Synopsis

Rigorous yet accessible, this resurrected classic in modern algebra is an exposition on the structural complexities of linear associative algebras from one of the twentieth century's most influential algebraic pioneers.
 

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

Core Features & Technical Benefits

• Delivers a comprehensive treatment of linear associative algebras and advanced mathematical structures, making it an essential reference for graduate-level study.
• An essential abstract algebra textbook that significantly reduces reliance on classical ideal theory.
• Advanced structural decomposition guides readers through a meticulous breakdown of algebraic fundamental topics, including Wedderburn structure theory, commutator subalgebras, automorphisms, splitting fields, and index reduction factors, before advancing into deeper structural analysis.
• Pioneering algebraic methodologies reveal with clarity a strong foundation in crossed products, cyclic algebras, and division algebra factorization, key subjects in higher algebra and algebra research.
• Connects algebraic representation theory to applications involving Riemann matrices and involutorial simple algebras, expanding its value beyond pure theory.
• Showcases A. Adrian Albert’s pioneering methods and historic contributions, offering readers a seminal graduate mathematics reference in linear associative algebra.
• Includes a comprehensive bibliography, making this once out-of-print classic an invaluable resource for study, scholarship, and long-term mathematical reference.  

Structure of Algebras remains an indispensable resource for anyone seeking a deeper understanding of associative algebras, algebraic structures, and the evolution of twentieth-century mathematical thought. 

About this title

About the Author

Abraham Adrian Albert was an American mathematician. In 1939, he received the American Mathematical Society's Cole Prize in Algebra for his work on Riemann matrices.

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.

Edition details

• Publisher: Dover Publications
• Publication date: 2026
• Language: English
• ISBN 10: 0486856372
• ISBN 13: 9780486856377
• Binding: Paperback
• Number of pages: 224