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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