Abstract Algebra, 3rd Edition
July 2003, ©2004
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- Accessible to undergraduates yet its scope and depth also make it ideal for courses at the graduate level.
- Over 1950 exercises, many with multiple parts, ranging in scope from routine to fairly sophisticated, and ranging in purpose from basic application of text material to exploration of important theoretical or computational techniques.
- The structure of the book permits instructors and students to pursue certain areas from their beginnings to an in-depth treatment, or to survey a wider range of areas, seeing how various themes recur and how different structures are related.
- The emphasis throughout is to motivate the introduction and development of important algebraic concepts using as many examples as possible. The wealth of examples helps to ground the theory, explain its application, and help develop the student's intuition.
- Contains many topics not usually found in introductory texts. Students are able to see how these fit naturally into the main themes of algebra. Examples of these topics include:
- Rings of algebraic integers
- Semidirect products and the theory of extensions
- Criteria for Principal Ideal Domains
- Criteria for the solvability of a quintic
- Dedekind Domains
- Algorithm for determining whether an ideal in a polynomial ring over a field is a prime ideal
- Affine schemes
- Galois cohomology
- Burnside's Theorem on the solvability of groups of order paqb