A central simple algebra over a field k is a finite dimensional k-algebra with center k that does not have any proper two-sided ideals, explain Berhuy and Oggier (both mathematics, North Dakota State U.). They introduce the theory of central simple algebras at a level accessible to graduate mathematics students, starting from scratch and including fundamental concepts such as splitting fields, Bayer group, crossed-product algebras, index and exponent, and algebras with involution. The exposition is rather classical, they say, though they focus on explicit techniques and examples, most of them from coding theory. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)
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Gregory Berhuy, Universite Joseph Fourier, Grenoble, France
Frederique Oggier, Nanyang Technological University, Singapore, Singapore
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Hardback. Zustand: New. Central simple algebras arise naturally in many areas of mathematics. They are closely connected with ring theory, but are also important in representation theory, algebraic geometry and number theory. Recently, surprising applications of the theory of central simple algebras have arisen in the context of coding for wireless communication. The exposition in the book takes advantage of this serendipity, presenting an introduction to the theory of central simple algebras intertwined with its applications to coding theory. Many results or constructions from the standard theory are presented in classical form, but with a focus on explicit techniques and examples, often from coding theory. Topics covered include quaternion algebras, splitting fields, the Skolem-Noether Theorem, the Brauer group, crossed products, cyclic algebras and algebras with a unitary involution. Code constructions give the opportunity for many examples and explicit computations. This book provides an introduction to the theory of central algebras accessible to graduate students, while also presenting topics in coding theory for wireless communication for a mathematical audience. It is also suitable for coding theorists interested in learning how division algebras may be useful for coding in wireless communication. Bestandsnummer des Verkäufers LU-9780821849378
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Hardback. Zustand: New. Central simple algebras arise naturally in many areas of mathematics. They are closely connected with ring theory, but are also important in representation theory, algebraic geometry and number theory. Recently, surprising applications of the theory of central simple algebras have arisen in the context of coding for wireless communication. The exposition in the book takes advantage of this serendipity, presenting an introduction to the theory of central simple algebras intertwined with its applications to coding theory. Many results or constructions from the standard theory are presented in classical form, but with a focus on explicit techniques and examples, often from coding theory. Topics covered include quaternion algebras, splitting fields, the Skolem-Noether Theorem, the Brauer group, crossed products, cyclic algebras and algebras with a unitary involution. Code constructions give the opportunity for many examples and explicit computations. This book provides an introduction to the theory of central algebras accessible to graduate students, while also presenting topics in coding theory for wireless communication for a mathematical audience. It is also suitable for coding theorists interested in learning how division algebras may be useful for coding in wireless communication. Bestandsnummer des Verkäufers LU-9780821849378
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