Basic Notions of Algebra
(Sprache: Englisch)
This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on...
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This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Comparable in style with Hermann Weyl's evergreen essay The Classical Groups, Shafarevich's new book is sure to become required reading for mathematicians, from beginners to experts.
Inhaltsverzeichnis zu „Basic Notions of Algebra “
What is Algebra?.- Fields.- Commutative Rings.- Homomorphisms and Ideals.- Modules.- Algebraic Aspects of Dimension.- The Algebraic View of Infinitesimal Notions.- Noncommutative Rings.- Modules over Noncommutative Rings.- Semisimple Modules and Rings.- Division Algebras of Finite Rank.- The Notion of a Group.- Examples of Groups: Finite Groups.- Examples of Groups: Infinite Discrete Groups.- Examples of Groups: Lie Groups and Algebraic Groups.- General Results of Group Theory.- Group Representations.- Some Applications of Groups.- Lie Algebras and Nonassociative Algebra.- Categories.- Homological Algebra.- K-theory.
Bibliographische Angaben
- Autor: Igor R. Shafarevich
- 2005, 2005., 260 Seiten, Maße: 16,4 x 24,3 cm, Gebunden, Englisch
- Herausgegeben:Shafarevich, Igor R.; Kostrikin, Aleksej I.;Übersetzung:Reid, M.
- Herausgegeben: Aleksej I. Kostrikin, Igor R. Shafarevich
- Übersetzer: M. Reid
- Verlag: Springer
- ISBN-10: 3540251774
- ISBN-13: 9783540251774
- Erscheinungsdatum: 13.04.2005
Sprache:
Englisch
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