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Book Summary of A First Course in Abstract Algebra
Considered a classic by many, A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.
Features
Table Of Contents
GROUPS AND SUBGROUPS.
Features
- This classical approach to abstract algebra focuses on applications.
- The text is geared toward high-level courses at schools with strong mathematics programs.
- Accessible pedagogy includes historical notes written by Victor Katz, an authority on the history of math.
- By opening with a study of group theory, this text provides students with an easy transition to axiomatic mathematics.
Table Of Contents
GROUPS AND SUBGROUPS.
- Introduction and Examples.
- Binary Operations.
- Isomorphic Binary Structures.
- Groups.
- Subgroups.
- Cyclic Groups.
- Generators and Cayley Digraphs.
- Groups of Permutations.
- Orbits, Cycles, and the Alternating Groups.
- Cosets and the Theorem of Lagrange.
- Direct Products and Finitely Generated Abelian Groups.
- Plane Isometries.
- Homomorphisms.
- Factor Groups.
- Factor-Group Computations and Simple Groups.
- Group Action on a Set.
- Applications of G-Sets to Counting.
- Rings and Fields.
- Integral Domains.
- Fermat's and Euler's Theorems.
- The Field of Quotients of an Integral Domain.
- Rings of Polynomials.
- Factorization of Polynomials over a Field.
- Noncommutative Examples.
- Ordered Rings and Fields.
- Homomorphisms and Factor Rings.
- Prime and Maximal Ideas.
- Gröbner Bases for Ideals.
- Introduction to Extension Fields.
- Vector Spaces.
- Algebraic Extensions.
- Geometric Constructions.
- Finite Fields.
- Isomorphism Theorems.
- Series of Groups.
- Sylow Theorems.
- Applications of the Sylow Theory.
- Free Abelian Groups.
- Free Groups.
- Group Presentations.
- Simplicial Complexes and Homology Groups.
- Computations of Homology Groups.
- More Homology Computations and Applications.
- Homological Algebra.
- Unique Factorization Domains.
- Euclidean Domains.
- Gaussian Integers and Multiplicative Norms.
- Automorphisms of Fields.
- The Isomorphism Extension Theorem.
- Splitting Fields.
- Separable Extensions.
- Totally Inseparable Extensions.
- Galois Theory.
- Illustrations of Galois Theory.
- Cyclotomic Extensions.
- Insolvability of the Quintic.
Details of Book: A First Course in Abstract Algebra
Book: | A First Course in Abstract Algebra |
Author: | John B. Fraleigh |
ISBN: | 8177589008 |
ISBN-13: | 9788177589009,978-8177589009 |
Binding: | Paperback |
Publishing Date: | 2003 |
Publisher: | Pearson Education |
Edition: | 7thEdition |
Number of Pages: | 530 |
Language: | English |
Dimensions: | 9.13 x 7.48 x 0.94 inches |
Weight: | 821 grams |
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