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A First Course in Abstract Algebra, 7/e
by John B. Fraleigh
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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.
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Features
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- 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.
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Contents
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- GROUPS AND SUBGROUPS.
- Introduction and Examples.
- Binary Operations.
- Isomorphic Binary Structures.
- Groups.
- Subgroups.
- Cyclic Groups.
- Generators and Cayley Digraphs.
- PERMUTATIONS, COSETS, AND DIRECT PRODUCTS.
- 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 AND FACTOR GROUPS.
- Homomorphisms.
- Factor Groups.
- Factor-Group Computations and Simple Groups.
- Group Action on a Set.
- Applications of G-Sets to Counting.
- RINGS AND FIELDS.
- 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.
- IDEALS AND FACTOR RINGS.
- Homomorphisms and Factor Rings.
- Prime and Maximal Ideas.
- Gröbner Bases for Ideals.
- EXTENSION FIELDS.
- Introduction to Extension Fields.
- Vector Spaces.
- Algebraic Extensions.
- Geometric Constructions.
- Finite Fields.
- ADVANCED GROUP THEORY.
- Isomorphism Theorems.
- Series of Groups.
- Sylow Theorems.
- Applications of the Sylow Theory.
- Free Abelian Groups.
- Free Groups.
- Group Presentations.
- GROUPS IN TOPOLOGY.
- Simplicial Complexes and Homology Groups.
- Computations of Homology Groups.
- More Homology Computations and Applications.
- Homological Algebra.
- FACTORIZATION.
- Unique Factorization Domains.
- Euclidean Domains.
- Gaussian Integers and Multiplicative Norms.
- MORPHISMS AND GALOIS THEORY.
- 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.
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Book Details
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Author
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John B. Fraleigh
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ISBN
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9788177589009
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Pages
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590
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Imprint
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Pearson Education
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Binding
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Paperback
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© Year
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2003
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Weight
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0.774 Kg
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