A Course On Abstract Algebra - Hardcover

Eie, Minking

Hardcover

ISBN 10: 9814271888 ISBN 13: 9789814271882

Publisher: Wspc, 2010

Synopsis

This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions. This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.

About this title

From the Back Cover

This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the author's lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions.

This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.

Edition details

• Publisher: Wspc
• Publication date: 2010
• Language: English
• ISBN 10: 9814271888
• ISBN 13: 9789814271882
• Binding: Hardcover
• Number of pages: 372