Algebra: Groups, Rings, Polynomials and Fields

Provides an introduction to the world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarises the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems and come equipped with hints when needed. Appropriate for both self-study and the classroom, the material is efficiently arranged so that milestones such as the Sylow theorems and Galois theory can be reached in one semester. Table of Contents Cover--------------------------------------------------------- 1 Title page---------------------------------------------------- 4 Contents------------------------------------------------------ 8 Preface------------------------------------------------------ 12 Chapter 1. Arithmetic----------------------------------------- 16 Chapter 2. Groups--------------------------------------------- 48 Chapter 3. Rings--------------------------------------------- 146 Chapter 4. Field theory-------------------------------------- 208 Index-------------------------------------------------------- 266 Back Cover--------------------------------------------------- 273 Preface Sepanski offers an introductory undergraduate algebra text beginning with integers and modular arithmetic and following with group theory, ring theory, and field theory. The final section of the text deals with Sylow's theorems and Galois theory. Included are more than 750 exercises in a range of skill levels including some complex problems rarely seen in first course texts. Annotation 2011 Book News, Inc., Portland, OR (booknews.com)