
Course On Abstract Algebra, A
World Scientific Publishing Co Pte Ltd
Published on 3. March 2010
Book
Hardback
372 pages
978-981-4271-88-2 (ISBN)
Description
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.
More details
Language
English
Place of publication
Singapore
Singapore
Target group
College/higher education
Advanced undergraduates and academics in pure mathematics.
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 25 mm
Weight
689 gr
ISBN-13
978-981-4271-88-2 (9789814271882)
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Schweitzer Classification
Persons
Content
Algebraic Structure of Numbers; Sets and Functions; Basic Group Theory; Elementary Group Theory; Group Homomorphisms; Direct Products of Finite Abelian Groups; Sylow's Theorems and Applications; Symmetric Groups; Basic Ring Theory; Special Properties of Rings; Field Theory; Basic Galois Theory.