Contemporary abstract algebra /
Gallian, Joseph A.
Contemporary abstract algebra / Joseph A. Gallian, University of Minnesota Duluth. - Ninth edition. - Boston, MA : Cengage Learning, c2017. - xvi, 557, 43 pages : illustrations ; 24 cm
Includes bibliographical references and indexes.
Integers and equivalence relations -- Preliminaries -- Introduction to groups -- Groups -- Finite groups; subgroups -- Cyclic groups -- Permutation groups -- Isomorphisms -- Cosets and Lagrange's theorem -- External direct products -- Normal subgroups and factor groups -- Group homomorphisms -- Fundamental theorem of finite abelian groups -- Rings -- Introduction to rings -- Integral domains -- Ideals and factor rings -- Ring homomorphisms -- Polynomial rings -- Factorization of polynomials -- Divisibility in integral domains -- Fields -- Vector spaces -- Extension fields -- Algebraic extensions -- Finite fields -- Geometric constructions -- Special topics -- Sylow theorems -- Finite simple groups -- Generators and relations -- Symmetry groups -- Frieze groups and crystallographic groups -- Symmetry and counting -- Cayley digraphs of groups -- Introduction to algebraic coding theory -- An introduction to galois theory -- Cyclotomic extensions.
9781305657960 (hardback) 1305657969 (hardback)
2015954307
Algebra, Abstract
QA162 / G13 2017
Contemporary abstract algebra / Joseph A. Gallian, University of Minnesota Duluth. - Ninth edition. - Boston, MA : Cengage Learning, c2017. - xvi, 557, 43 pages : illustrations ; 24 cm
Includes bibliographical references and indexes.
Integers and equivalence relations -- Preliminaries -- Introduction to groups -- Groups -- Finite groups; subgroups -- Cyclic groups -- Permutation groups -- Isomorphisms -- Cosets and Lagrange's theorem -- External direct products -- Normal subgroups and factor groups -- Group homomorphisms -- Fundamental theorem of finite abelian groups -- Rings -- Introduction to rings -- Integral domains -- Ideals and factor rings -- Ring homomorphisms -- Polynomial rings -- Factorization of polynomials -- Divisibility in integral domains -- Fields -- Vector spaces -- Extension fields -- Algebraic extensions -- Finite fields -- Geometric constructions -- Special topics -- Sylow theorems -- Finite simple groups -- Generators and relations -- Symmetry groups -- Frieze groups and crystallographic groups -- Symmetry and counting -- Cayley digraphs of groups -- Introduction to algebraic coding theory -- An introduction to galois theory -- Cyclotomic extensions.
9781305657960 (hardback) 1305657969 (hardback)
2015954307
Algebra, Abstract
QA162 / G13 2017