The Resource A first course in abstract algebra, John B. Fraleigh ; historical notes by Victor Katz
A first course in abstract algebra, John B. Fraleigh ; historical notes by Victor Katz
Resource Information
The item A first course in abstract algebra, John B. Fraleigh ; historical notes by Victor Katz represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Yuma County Library District.This item is available to borrow from 1 library branch.
Resource Information
The item A first course in abstract algebra, John B. Fraleigh ; historical notes by Victor Katz represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Yuma County Library District.
This item is available to borrow from 1 library branch.
 Edition
 7th ed.
 Extent
 xii, 520 p.
 Contents

 Sets and relations
 I. Groups and subgroups. Introduction and examples ; Binary operations ; Isomorphic binary structures ; Groups ; Subgroups ; Cyclic groups ; Generating sets and Cayley Digraphs
 II. 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
 III. Homomorphisms and factor groups. Homomorphisms ; Factor groups ; Factorgroup computations and simple groups ; Group action on a set ; Applications of Gsets to counting
 IV. 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
 V. Ideals and factor rings. Homomorphisms and factor rings ; Prime and maximal ideas ; Gröbner bases for ideals
 VI. Extension fields. Introduction to extension fields ; Vector spaces ; Algebraic extensions ; Geometric constructions ; Finite fields
 VII. Advanced group theory. Isomorphism theorems ; Series of groups ; Sylow theorems ; Applications of the Sylow theory ; Free Abelian groups ; Free groups ; Group presentations
 VIII. Groups in topology. Simplicial complexes and homology groups ; Computations of homology groups ; More homology computations and applications ; Homological algebra
 IX. Factorization. Unique factorization domains ; Euclidean domains ; Gaussian integers and multiplicative norms
 X. Automorphisms 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
 Appendix: Matrix algebra
 Isbn
 9780201763904
 Label
 A first course in abstract algebra
 Title
 A first course in abstract algebra
 Statement of responsibility
 John B. Fraleigh ; historical notes by Victor Katz
 Language
 eng
 Cataloging source
 DLC
 http://library.link/vocab/creatorName
 Fraleigh, John B
 Dewey number
 512/.02
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA162
 LC item number
 .F7 2003
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Katz, Victor J
 http://library.link/vocab/subjectName
 Algebra, Abstract
 Label
 A first course in abstract algebra, John B. Fraleigh ; historical notes by Victor Katz
 Bibliography note
 Includes bibliographical references (p. 483485) and index
 Contents
 Sets and relations  I. Groups and subgroups. Introduction and examples ; Binary operations ; Isomorphic binary structures ; Groups ; Subgroups ; Cyclic groups ; Generating sets and Cayley Digraphs  II. 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  III. Homomorphisms and factor groups. Homomorphisms ; Factor groups ; Factorgroup computations and simple groups ; Group action on a set ; Applications of Gsets to counting  IV. 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  V. Ideals and factor rings. Homomorphisms and factor rings ; Prime and maximal ideas ; Gröbner bases for ideals  VI. Extension fields. Introduction to extension fields ; Vector spaces ; Algebraic extensions ; Geometric constructions ; Finite fields  VII. Advanced group theory. Isomorphism theorems ; Series of groups ; Sylow theorems ; Applications of the Sylow theory ; Free Abelian groups ; Free groups ; Group presentations  VIII. Groups in topology. Simplicial complexes and homology groups ; Computations of homology groups ; More homology computations and applications ; Homological algebra  IX. Factorization. Unique factorization domains ; Euclidean domains ; Gaussian integers and multiplicative norms  X. Automorphisms 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  Appendix: Matrix algebra
 Control code
 ocm49312505
 Dimensions
 24 cm.
 Edition
 7th ed.
 Extent
 xii, 520 p.
 Isbn
 9780201763904
 Lccn
 2002019357
 Other physical details
 ill.
 System control number
 (OCoLC)49312505
 Label
 A first course in abstract algebra, John B. Fraleigh ; historical notes by Victor Katz
 Bibliography note
 Includes bibliographical references (p. 483485) and index
 Contents
 Sets and relations  I. Groups and subgroups. Introduction and examples ; Binary operations ; Isomorphic binary structures ; Groups ; Subgroups ; Cyclic groups ; Generating sets and Cayley Digraphs  II. 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  III. Homomorphisms and factor groups. Homomorphisms ; Factor groups ; Factorgroup computations and simple groups ; Group action on a set ; Applications of Gsets to counting  IV. 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  V. Ideals and factor rings. Homomorphisms and factor rings ; Prime and maximal ideas ; Gröbner bases for ideals  VI. Extension fields. Introduction to extension fields ; Vector spaces ; Algebraic extensions ; Geometric constructions ; Finite fields  VII. Advanced group theory. Isomorphism theorems ; Series of groups ; Sylow theorems ; Applications of the Sylow theory ; Free Abelian groups ; Free groups ; Group presentations  VIII. Groups in topology. Simplicial complexes and homology groups ; Computations of homology groups ; More homology computations and applications ; Homological algebra  IX. Factorization. Unique factorization domains ; Euclidean domains ; Gaussian integers and multiplicative norms  X. Automorphisms 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  Appendix: Matrix algebra
 Control code
 ocm49312505
 Dimensions
 24 cm.
 Edition
 7th ed.
 Extent
 xii, 520 p.
 Isbn
 9780201763904
 Lccn
 2002019357
 Other physical details
 ill.
 System control number
 (OCoLC)49312505
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