Coverart for item
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

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
Creator
Contributor
Subject
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
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 483-485) 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 ; Factor-group computations and simple groups ; Group action on a set ; Applications of G-sets 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
Publication
Bibliography note
Includes bibliographical references (p. 483-485) 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 ; Factor-group computations and simple groups ; Group action on a set ; Applications of G-sets 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

Library Locations

    • Academic LibraryBorrow it
      2020 S. Avenue 8E, Yuma, AZ, 85366, US
      32.6910976 -114.6289698
Processing Feedback ...