Free Ideal Rings and Localization in Gener...

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Sprache: Englisch

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Beschreibung

Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.

Über den Autor

Paul Cohn is a Emeritus Professor of Mathematics at the University of London and Honorary Research Fellow at University College London.

Inhaltsverzeichnis

Preface; Note to the reader; Terminology, notations and conventions used; List of special notation; 0. Preliminaries on modules; 1. Principal ideal domains; 2. Firs, semifirs and the weak algorithm; 3. Factorization; 4. 2-firs with a distributive factor lattice; 5. Modules over firs and semifirs; 6. Centralizers and subalgebras; 7. Skew fields of fractions; Appendix; Bibliography and author index; Subject index.

Details

Erscheinungsjahr:	2006
Fachbereich:	Arithmetik & Algebra
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
ISBN-13:	9780521853378
ISBN-10:	0521853370
Sprache:	Englisch
Einband:	Gebunden
Autor:	Cohn, P. M
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	235 x 157 x 36 mm
Von/Mit:	P. M Cohn
Erscheinungsdatum:	08.06.2006
Gewicht:	1,002 kg