Fundamentals of abstract algebra
著者
書誌事項
Fundamentals of abstract algebra
（International series in pure and applied mathematics）
McGraw-Hill, c1997
大学図書館所蔵 件 / 全11件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. [602]-604) and index
内容説明・目次
内容説明
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.
目次
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
「Nielsen BookData」 より
