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First Course in Abstract Algebra Rings, Groups and Fields

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ISBN-10: 1584885157

ISBN-13: 9781584885153

Edition: 2nd 2005 (Revised)

Authors: Marlow Anderson, Todd Feil

List price: $97.95
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Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there is more natural-and ultimately more effective.Authors Anderson and Feil developed A First Course in Abstract Algebra: Rings, Groups and Fields based upon that conviction. The text begins with ring theory, building upon students' familiarity with integers and polynomials. Later, when students have become more experienced, it introduces groups. The…    
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Book details

List price: $97.95
Edition: 2nd
Copyright year: 2005
Publisher: CRC Press LLC
Publication date: 1/27/2005
Binding: Hardcover
Pages: 696
Size: 7.56" wide x 9.65" long x 1.54" tall
Weight: 2.442
Language: English

The natural numbers
The integers
Modular arithmetic
Polynomials with rational coefficients
Factorization of polynomials
Subrings and unity
Integral domains and fields
Polynomials over a field
Associates and irreducibles
Factorization and ideals
Principal ideal domains
Primes and unique factorization
Polynomials with integer coefficients
Euclidean domains
Ring homomorphisms
The kernel
Rings of cosets
The isomorphism theorem for rings
Maximal and prime ideals
The Chinese remainder theorem
Symmetries of figures in the plane
Symmetries of figures in space
Abstract groups
Cyclic groups
Group homomorphisms
Group isomorphisms
Permutations and Cayley's theorem
More about permutations
Cosets and Lagrange's theorem
Groups of cosets
The isomorphism theorem for groups
The alternating groups
Fundamental theorem for finite Abelian groups
Solvable groups
Constructions with compass and straightedge
Constructibility and quadratic field extensions
The impossibility of certain constructions
Vector spaces I
Vector spaces II
Field extensions and Kronecker's theorem
Algebraic field extensions
Finite extensions and constructibility revisited
The splitting field
Finite fields
Galois groups
The fundamental theorem of Galois theory
Solving polynomials by radicals