1st course in Abstract Algebra 7E - Fraleigh

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1、Instructor’sSolutionsManualtoaccompanyAFirstCourseinAbstractAlgebraSeventhEditionJohnB.FraleighUniversityofRhodeIslandPrefaceThismanualcontainssolutionstoallexercisesinthetext,exceptthoseodd-numberedexercisesforwhichfairlylengthycompletesolutionsaregivenintheanswersattheback

2、ofthetext.Thenreferenceissimplygiventothetextanswerstosavetyping.Ipreparedthesesolutionsmyself.WhileItriedtobeaccurate,therearesuretobetheinevitablemistakesandtypos.Anauthorreadingproofrendstoseewhatheorshewantstosee.However,theinstructorshouldfindthismanualadequateforthepurp

3、oseforwhichitisintended.Morgan,VermontJ.B.FJuly,2002iiiCONTENTS0.SetsandRelations1I.GroupsandSubgroups1.IntroductionandExamples42.BinaryOperations73.IsomorphicBinaryStructures94.Groups135.Subgroups176.CyclicGroups217.GeneratorsandCayleyDigraphs24II.Permutations,Cosets,andDir

4、ectProducts8.GroupsofPermutations269.Orbits,Cycles,andtheAlternatingGroups3010.CosetsandtheTheoremofLagrange3411.DirectProductsandFinitelyGeneratedAbelianGroups3712.PlaneIsometries42III.HomomorphismsandFactorGroups13.Homomorphisms4414.FactorGroups4915.Factor-GroupComputation

5、sandSimpleGroups5316.GroupActiononaSet5817.ApplicationsofG-SetstoCounting61IV.RingsandFields18.RingsandFields6319.IntegralDomains6820.Fermat’sandEuler’sTheorems7221.TheFieldofQuotientsofanIntegralDomain7422.RingsofPolynomials7623.FactorizationofPolynomialsoveraField7924.Nonc

6、ommutativeExamples8525.OrderedRingsandFields87V.IdealsandFactorRings26.HomomorphismsandFactorRings8927.PrimeandMaximalIdeals9428.Gr¨obnerBasesforIdeals99iiiVI.ExtensionFields29.IntroductiontoExtensionFields10330.VectorSpaces10731.AlgebraicExtensions11132.GeometricConstructio

7、ns11533.FiniteFields116VII.AdvancedGroupTheory34.IsomorphismTheorems11735.SeriesofGroups11936.SylowTheorems12237.ApplicationsoftheSylowTheory12438.FreeAbelianGroups12839.FreeGroups13040.GroupPresentations133VIII.GroupsinTopology41.SimplicialComplexesandHomologyGroups13642.Co

8、mputationsofHomologyGroups13843.MoreHomologyComputationsandApplications1404