First Course in Abstract Algebra Rings, Groups and Fields

Name: First Course in Abstract Algebra Rings, Groups and Fields
Availability: OutOfStock
ISBN: 9781584885153

ISBN-10: 1584885157

ISBN-13: 9781584885153

Edition: 2nd 2005 (Revised)

Authors: Marlow Anderson, Todd Feil

List price: $97.95

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Description:

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…

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



Rings



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



Subgroups



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