Algebraic Structures
(Sprache: Englisch)
In algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition - the basic operations of algebra - are studied. Essentially, no previous knowledge is...
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Produktinformationen zu „Algebraic Structures “
In algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition - the basic operations of algebra - are studied. Essentially, no previous knowledge is required, it is only assumed as background that the reader has learned some linear algebra over the real numbers.Dieses Lehrbuch, verfasst von einem anerkannten amerikanischen Mathematiker, ist eine unkonventionelle Einführung in die Algebra. Es gibt vier grundlegende Strukturen in der Algebra: Gruppen, Ringe, Körper und Moduln. Das Buch behandelt die Theorie dieser Strukturen und beschreibt die Verknüpfungsregeln, die grundlegenden Operationen der Algebra. Die Darstellung ist elementar: es werden nur Kenntnisse der Linearen Algebra vorausgesetzt, weitere Fachkenntnisse sind nicht erforderlich.
Klappentext zu „Algebraic Structures “
The laws of composition include addition and multiplication of numbers or func tions. These are the basic operations of algebra. One can generalize these operations to groups where there is just one law. The theory of this book was started in 1800 by Gauss, when he solved the 2000 year-old Greek problem about constructing regular n-gons by ruler and compass. The theory was further developed by Abel and Galois. After years of development the theory was put in the present form by E. Noether and E. Artin in 1930. At that time it was called modern algebra and concentrated on the abstract exposition of the theory. Nowadays there are too many examples to go into their details. I think the student should study the proofs of the theorems and not spend time looking for solutions to tricky exercises. The exercises are designed to clarify the theory. In algebra there are four basic structures; groups, rings, fields and modules. We present the theory of these basic structures. Hopefully this will give a good introduc tion to modern algebra. I have assumed as background that the reader has learned linear algebra over the real numbers but this is not necessary.
Inhaltsverzeichnis zu „Algebraic Structures “
- Fundamentals of Groups- Fundamentals of Rings and Fields
- Modules
- A Little More Group Theory
- Field Theory
- More Field Theory
- Modern Linear Algebra
- Quadratic and Alternative Forms
- Ring and Field Extensions
- Noetherian Rings and Localization
- Dedekind Domains
- Representations of Groups
- More Modules
- Categories
- Completion
- Lie Algebra
- The Clifford Algebra
- Commutative Rings
- Logic
- Tor's
Autoren-Porträt von George R. Kempf
Prof. Georg Kempf lehrt an der Johns Hopkins University; Baltimore, Maryland, USA.
Bibliographische Angaben
- Autor: George R. Kempf
- 1995, Softcover reprint of the original 1st ed. 1995, IX, 166 Seiten, Maße: 22,9 cm, Kartoniert (TB), Englisch
- Verlag: Vieweg+Teubner
- ISBN-10: 3528065834
- ISBN-13: 9783528065836
Sprache:
Englisch
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