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＜電子ブック＞
Finite-Dimensional Division Algebras over Fields / by Nathan Jacobson

版	1st ed. 1996.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1996
本文言語	英語
大きさ	VIII, 284 p : online resource
著者標目	*Jacobson, Nathan author SpringerLink (Online service)
件　名	LCSH:Algebra FREE:Algebra
一般注記	Skew Polynomials and Division Algebras -- Brauer Factor Sets and Noether Factor Sets -- Galois Descent and Generic Splitting Fields -- p-Algebras -- Simple Algebras with Involution Finite-dimensional division algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensio= nal algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brau= er-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts;they arose first in the study of the so-called "multiplication algebras of Riemann matrices". The largest part of the book is the fifth chapter, dealing with involu= torial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution;their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm. Corrections of the 1st edition (1996) carried out on behalf of N. Jacobson (deceased) by Prof. P.M. Cohn (UC London, UK) HTTP:URL=https://doi.org/10.1007/978-3-642-02429-0

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