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Inhaltsangabe
This book is an introduction to the theory of non-commutative algebra. The core of the book is suitable for a one-semester course for graduate students. The approach, which is more homological than ring-theoretic, clarifies the subject and its relation to other important areas of mathematics, including K-theory, homological algebra, and representation theory. The main part of the book begins with a brief review of background material; the first chapter covers the basics of semi-simple modules and rings, including the Wedderbum structure theorem; chapter two discusses the Jacobson radical, giving several different views; chapter three develops the theory of central simple algebras, including proofs of the Skolem-Noether and Double Centralizer theorems, with two famous theorems of Wedderburn and Frobenius given as applications; and chapter four is an introduction to the Brauer group and its relation to cohomology. The remaining chapters introduce several special topics: the notion of primitive ring is developed along lines parallel to that of simple rings; the representation theory of fugte groups is combined with the Wedderburn Structure Theorem to prove Burnside's Theorem; the global dimension of a ring is studied using Kaplansky's elementary point of view; and the Brauer group of a commutative ring is introduced. Problems throughout the book provide concrete examples, applications and amplifications of the text; a set of supplementary problems explores further topics and can serve as starting points for student projects.
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This book is an introduction to the theory of non-commutative algebra. The core of the book is suitable for a one-semester course for graduate students. The approach, which is more homological than ring-theoretic, clarifies the subject and its relation to other important areas of mathematics, including K-theory, homological algebra, and representation theory. The main part of the book begins with a brief review of background material; the first chapter covers the basics of semi-simple modules and rings, including the Wedderbum structure theorem; chapter two discusses the Jacobson radical, giving several different views; chapter three develops the theory of central simple algebras, including proofs of the Skolem-Noether and Double Centralizer theorems, with two famous theorems of Wedderburn and Frobenius given as applications; and chapter four is an introduction to the Brauer group and its relation to cohomology. The remaining chapters introduce several special topics: the notion of primitive ring is developed along lines parallel to that of simple rings; the representation theory of fugte groups is combined with the Wedderburn Structure Theorem to prove Burnside's Theorem; the global dimension of a ring is studied using Kaplansky's elementary point of view; and the Brauer group of a commutative ring is introduced. Problems throughout the book provide concrete examples, applications and amplifications of the text; a set of supplementary problems explores further topics and can serve as starting points for student projects.
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Suchergebnisse für Noncommutative algebra: v. 144 (Graduate Texts in Mathematic...
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Noncommutative algebra. Graduate Texts in Mathematics; 144.
Verlag:
New York, Springer-Verlag, 1993
ISBN 10: 354094057X
ISBN 13: 9783540940579
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Hardcover
Anbieter: Antiquariat Bookfarm, Löbnitz, Deutschland
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Hardcover. xiv, 223 p. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-04627 354094057X Sprache: Englisch Gewicht in Gramm: 550. Bestandsnummer des Verkäufers 2490865
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Noncommutative Algebra.
ISBN 10: 354094057X
ISBN 13: 9783540940579
Gebraucht
Hardcover
Anbieter: Antiquariat Smock, Freiburg, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Zustand: Gut. Formateinband: Pappband / gebundene Ausgabe XIV, 223 S. (24 cm) Gebundene Ausgabe; 1. Aufl.; (Mit 13 Abbildungen); Am Rücken minimal aufgehellt; sonst gut und sauber erhalten! Sprache: Englisch Gewicht in Gramm: 600 [Stichwörter: Nichtkommutative Algebra, Semisimple modules and Rings and the Wedderburn Structure Theorem, The Jacobson Radical, The Brauer Group, Primitive Rings and the Density Theorem, Burnside's Theorem and Reperesentations of Finite Groups, The global dimension of ring, The Brauer Group of a Communatative Ring etc.]. Bestandsnummer des Verkäufers 62204
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Noncommutative Algebra (Graduate Texts in Mathematics)
Anbieter: Buchpark, Trebbin, Deutschland
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Zustand: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher. Bestandsnummer des Verkäufers 41565873/202
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