Fundamentals of Abstract Algebra
McGraw-Hill Professional (Publisher)
Published on 28. February 1997
Book
Hardback
636 pages
978-0-07-040035-1 (ISBN)
Description
For use in your advanced abstract algebra course, Fundamentals of Abstract Algebra takes a blended theory and applications approach. Each chapter consists of definitions, theorems, proofs, and corollaries. Throughout the text you will find numerous examples that illustrate the concepts, historical background on the development of abstract algebra, and profiles of notable mathematicians.
More details
Language
English
Place of publication
United States
Publishing group
McGraw-Hill Education - Europe
Target group
College/higher education
Illustrations
index
Dimensions
Height: 241 mm
Width: 168 mm
Thickness: 31 mm
Weight
953 gr
ISBN-13
978-0-07-040035-1 (9780070400351)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Content
CHAPTER 1: Sets, Relations, and IntegersSetsIntegersRelationsPartially Ordered SetFunctionsBinary OperationsCHAPTER 2: Introduction to GroupsElementary Properties of GroupsCHAPTER 3: Permution GroupsPermution GroupsCHAPTER 4: Subgroups and Normal SubgroupsSubgroupsCyclic GroupsLagrange's TheoremNormal Subgroups and Quotient GroupsCHAPTER 5: Homomorphisms and Isomorphisms of GroupsHomomorphisms of GroupsIsomorphisms and Correspondence TheoremsGroups D4 and Q8Group ActionsCHAPTER 7: Sylow TheoremConjugacy ClassesCauchy Theorem and p-groupsSylow TheoremsSome Applications of the Sylow TheoremCHAPTER 8: Solvable and Nilpotent GroupsSolvable Groups Nilpotent GroupsCHAPTER 9: Finitely Generated Abelian GroupsFinite Abelian GroupsFinitely Generated Abelian GroupsCHAPTER 10: Introduction to RingsElementary PropertiesSome Important RingsCHAPTER 11: Subrings, Ideals, and HomomorphismsSubrings and SubfieldsIdeals and Quotient RingsHomomorphisms and IsomrophismsCHAPTER 12: Extensions of RingsExtensions of RingsCHAPTER 13: Direct Sum of RingsComplete Direct Sum and Direct SumCHAPTER 14: Polynomial RingsPolynomial RingsCHAPTER 15: Euclidean DomainsEuclidean DomainsGreatest Common DivisorsPrime and Irreducible ElementsCHAPTER 16: Unique Factorization DomainsUnique Factorization DomainsFactorization of Polynomials over a UFDIrreducibility of PolynomialsCHAPTER 17: Maximal, Prime, and Primary IdealsMaximal, Prime and Primary IdealsJacobson Semisimple RingCHAPTER 18: Noetherian and Artinian RingsNoetherian and Artinian RingsCHAPTER 19: Modules and Vector SpacesModules and Vector SpacesCHAPTER 20: Matrix RingsFull Matrix Rings Triangular Matrix RingsCHAPTER 21: Field ExtensionsAlgebraic ExtensionsSplitting FieldsAlgebraically Colsed FieldsCHAPTER 22: Multiplicity of RootsMultiplicity of RootsCHAPTER 23: Finite FieldsFinite FieldsCHAPTER 24: Galois Theory and ApplicationsNormal ExtensionsGalois TheoryRoots of Unity and Cyclotomic PolynomialsSolution by RadicalsCHAPTER 25: Geometric Constructions Feometric ConstructionsCHAPTER 26: Binary CodesBinary CodesPolynomial and Cyclic CodesBose-Chauduri-Hocquenghem CodesCHAPTER 27: Groebner BasesAffine VaritiesGroebner BasesSelected BibliographyAnswers and Hints to Selected ExercisesIndex