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Cover: 9783662679739 | Abstract Algebra | Suitable for Self-Study or Online Lectures | Hien
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Abstract Algebra
Suitable for Self-Study or Online Lectures
Taschenbuch von Marco Hien
Sprache: Englisch

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Beschreibung
This book contains the basics of abstract algebra.

In addition to elementary algebraic structures such as groups, rings and solids, Galois theory in particular is developed together with its applications to the cyclotomic fields, finite fields or the question of the resolution of polynomial equations.

Special attention is paid to the natural development of the contents. Numerous intermediate explanations support this basic idea, show connections and help to better penetrate the underlying concepts.

The book is therefore particularly suitable for learning algebra in self-study or accompanying online lectures.
This book contains the basics of abstract algebra.

In addition to elementary algebraic structures such as groups, rings and solids, Galois theory in particular is developed together with its applications to the cyclotomic fields, finite fields or the question of the resolution of polynomial equations.

Special attention is paid to the natural development of the contents. Numerous intermediate explanations support this basic idea, show connections and help to better penetrate the underlying concepts.

The book is therefore particularly suitable for learning algebra in self-study or accompanying online lectures.
Über den Autor
After a postdoctoral year at the University of Chicago, Prof. Dr. Marco Hien initially worked at the University of Regensburg. Since 2010, he has been Professor of Algebra and Number Theory at the University of Augsburg with the research areas of algebraic geometry and algebraic analysis. In 2020, he received the "Prize for Good Teaching" from the Bavarian Ministry of Science.
Zusammenfassung

Develops the basic concepts and essential statements of abstract algebra up to the Galois theory step by step

Contains a variety of motivational intermediate statements and encourages self-reflection

Shows the effectiveness of the theory with many concrete examples

Inhaltsverzeichnis
Motivation and prerequisites.- Field extensions and algebraic elements.- Groups.- Group quotients and normal divisors.- Rings and ideals.- Euclidean rings, principal ideal rings, Noetherian rings.- Factorial rings.- Quotient fields for integrality domains.- Irreducible polynomials in factorial rings.- Galois theory (I) - Theorem A and its variant A'.- Intermezzo - explicit example.- Normal fields extensions.- Separability.- Galois theory (II) - The main theorem.- Cyclotomic fields.- Finite fields.- More group theory - Group operations and Sylow.- Resolvability of polynomial equations.
Details
Erscheinungsjahr: 2024
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: ix
307 S.
138 s/w Illustr.
2 farbige Illustr.
307 p. 140 illus.
2 illus. in color.
ISBN-13: 9783662679739
ISBN-10: 3662679736
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Hien, Marco
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 18 mm
Von/Mit: Marco Hien
Erscheinungsdatum: 07.08.2024
Gewicht: 0,487 kg
Artikel-ID: 127335309
Über den Autor
After a postdoctoral year at the University of Chicago, Prof. Dr. Marco Hien initially worked at the University of Regensburg. Since 2010, he has been Professor of Algebra and Number Theory at the University of Augsburg with the research areas of algebraic geometry and algebraic analysis. In 2020, he received the "Prize for Good Teaching" from the Bavarian Ministry of Science.
Zusammenfassung

Develops the basic concepts and essential statements of abstract algebra up to the Galois theory step by step

Contains a variety of motivational intermediate statements and encourages self-reflection

Shows the effectiveness of the theory with many concrete examples

Inhaltsverzeichnis
Motivation and prerequisites.- Field extensions and algebraic elements.- Groups.- Group quotients and normal divisors.- Rings and ideals.- Euclidean rings, principal ideal rings, Noetherian rings.- Factorial rings.- Quotient fields for integrality domains.- Irreducible polynomials in factorial rings.- Galois theory (I) - Theorem A and its variant A'.- Intermezzo - explicit example.- Normal fields extensions.- Separability.- Galois theory (II) - The main theorem.- Cyclotomic fields.- Finite fields.- More group theory - Group operations and Sylow.- Resolvability of polynomial equations.
Details
Erscheinungsjahr: 2024
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: ix
307 S.
138 s/w Illustr.
2 farbige Illustr.
307 p. 140 illus.
2 illus. in color.
ISBN-13: 9783662679739
ISBN-10: 3662679736
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Hien, Marco
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 18 mm
Von/Mit: Marco Hien
Erscheinungsdatum: 07.08.2024
Gewicht: 0,487 kg
Artikel-ID: 127335309
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