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The development avoids using group theory directly, while still pointing out analogies familiar to readers with group background. The final chapter on field extensions builds on earlier results and ends with a proof showing the impossibility of certain constructions using ruler and compasses. 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compasses.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},570230,1791879956,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144,"preview_page_count":4},2336478945519,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","# Introductionto AbstractAlgebra\n\n6s net(E0.30)  \nEditor:Walter Ledermann  \nThis book provides a simple introduction to the mostimportant concepts of modern algebra.There are chaptersdealing with integral domains,fields,rings,vector spacesand field extensions.The development proceeds withoutreference to groups,but those who are familiar with grouptheory will recognize many situations which arise.Thefinal chapter on field extensions uses many of the resultsdeveloped earlier in the book,and the conclusion containsa proof of the impossibility of various constructions withruler and compasses.  \nThe whole account is straightforward and is speciallywritten for those encountering abstract algebra for the firsttime.  \n\n| 99I07乙IES0  8II0E三  \u003Cbr>38IHSVONV7  \u003Cbr>H88 Lud 'N  \u003Cbr>01  \u003Cbr>u yooq s!41  \u003Cbr>a^oqe u   |  |  |  |\n| --- | --- | --- | --- |\n| 68L8001L  \u003Cbr>ON XOO8   |  | 371I1  \u003Cbr>叶 woypm4ug  \u003Cbr>29g   p4   |  |\n| oN SSV12  \u003Cbr>8·(15   |  |  |  |\n|  |  | XOHINV  \u003Cbr>0  \u003Cbr>'hUHdu72   |  |\n| 80V 20  \u003Cbr>86  \u003Cbr>Sd   |  |  | SZ697S  \u003Cbr>L∠6L83J℃2  \u003Cbr>↓L6  \u003Cbr>VW6   |\n\nVda397V LOVLSgV  \nOL NOILOnaOLNI  \n21  \n# LIBRARY OF MATHEMATICS\n\nedited by  \nWALTER LEDERMANN  \nD.Sc.,Ph.D.,R.F.S.Ed.,Professor ofMathematics,University of Sussex  \nLinear EquationsP.M.CohnSequences and SeriesJ.A.GreenDifferential CalculusP.J.HiltonElementary Differential  \nEquations and OperatorsG.E.H.ReuterPartial DerivativesP.J.HiltonComplex NumbersW.Ledermann  \nPrinciples of DynamicsM.B.GlauertElectrical and Mechanical  \nOscillationsD.S.Jones  \nVibrating SystemsR.F.ChisnellVibrating StringsD.R.Bland  \nFourier SeriesI.N.Sneddon  \nSolutions of Laplace's EquationD.R.Bland  \nSolid GeometryP.M.Cohn  \nNumerical ApproximationB.R.MortonIntegral CalculusW.LedermannSets and GroupsJ.A.Green  \nDifferential GeometryK.L.Wardle  \nProbability TheoryA.M.Arthurs  \nMultiple IntegralsW.Ledermann  \n(0  \nINTRODUCTION TOABSTRACT ALGEBRA  \nBY  \nC.R.J.CLAPHAM  \nLONDON:Routledge &Kegan Paul Ltd  \nNEW YORK:Dover Publications Inc  \nFirst Published 1969in Great Britain byRoutledge&Kegan Paul LtdBroadway House,68-74 Carter LaneLondon,E.C.4and in the U.S.A.byDover Publications Inc.180Varick StreetNew York,10014  \nC.R.J.Clapham,1969  \nNo part of this book may be reproducedin any form without permission fromthe publisher,except for the quotationof brief passages in criticism  \nSBN 710066260  \nPrinted in Great Britainby Willmer Brothers Limited,Birkenhead.  \n## Preface\n\nIn this book,I have aimed to provide a simple introduction tosome of the important concepts of modern algebra:integraldomains,fields,rings,vector spaces and field extensions.Thetheory of groups is not included,but is covered in the volumeSets and Groups by J.A.Green,in this Library,and thedevelopment here assumes no knowledge of groups.Thereader who is familiar with group theory,however,willrecognize many situations and analogies without having thempointed out to him.  \nThe whole account is straightforward and is written forthose who are making their first encounter with abstractalgebra.The final chapter on field extensions uses many of theresults developed earlier in the book and concludes with aproof of the impossibility of various constructions with rulerand compasses.  \nI should like to record here my thanks to Professor WalterLedermann who read an early draft of this book and madeseveral valuable suggestions.I am also grateful to Dr.BrianRotman for his helpful comments upon the manuscript.  \nThe University of Aberdeen  \nC.R.J.CLAPHAM  \nPreface  \npage v  \n1.Integral Domains  \n## 1.Introduction\n\n11  \n## 2.Operations\n\n2  \n## 3.Definition of an Integral Domain\n\n457  \n4.Elementary Properties  \n5.Further Examples of Integral Domains  \n6.The Residue Classes  \n## 2.Ordered and Well-ordered Integral Domains\n\n1114  \n7.Order  \n8.Well-Order  \n## 3.The Integers\n\n9.The Principles of Induction16  \n10.Divisibility17  \n11.Highest Common Factor19  \n12.Primes21  \n13.Unique Factorisation22vii  \nviii  \n## 4.Fields\n\n14.Definition of a Field  \n2","cbCaitqi8CkTetkp","https://ap.wps.com/l/cbCaitqi8CkTetkp","pdf",4158410,100,"English","# Preface\n# 1. Integral Domains\n## 1. Introduction\n## 2. Operations\n## 3. Definition of an Integral Domain\n## 4. Elementary Properties\n## 5. Further Examples of Integral Domains\n## 6. The Residue Classes\n## 2. Ordered and Well-ordered Integral Domains\n## 7. Order\n## 8. Well-Order\n# 3. The Integers\n## 9. The Principles of Induction\n## 10. Divisibility\n## 11. Highest Common Factor\n## 12. Primes\n## 13. Unique Factorisation\n# 4. Fields\n## 14. Definition of a Field\n## 15. Examples of Fields\n## 16. Subfields\n## 17. The Characteristic of a Field\n# 5. Rings\n## 18. Definition of a Ring\n## 19. Subrings\n## 20. Cosets\n## 21. Ideals\n## 22. Quotient Rings\n## 23. Maximal Ideals\n## 24. Homomorphisms\n# 6. Polynomials and Euclidean Rings\n## 25. Polynomials\n## 26. Divisibility\n## 27. Euclidean Rings\n## 28. Highest Common Factor\n## 29. Irreducible Elements\n## 30. Unique Factorisation\n## 31. Polynomials with Integer Coefficients\n# 7. Vector Spaces\n## 32. Definition of a Vector Space\n## 33. Definition of a Basis\n## 34. Dimension\n## 35. Coordinates","[{\"question\":\"What topics are covered in the book?\",\"answer\":\"The book introduces integral domains, fields, rings, vector spaces, and field extensions. It also develops related tools such as residue classes, polynomials, and vector space coordinates.\"},{\"question\":\"Does the book rely on group theory?\",\"answer\":\"The development does not reference groups. However, readers familiar with group theory will notice many situations and analogies.\"},{\"question\":\"How does the book conclude regarding ruler-and-compass constructions?\",\"answer\":\"The final chapter on field extensions uses earlier results and concludes with a proof of the impossibility of various constructions using a ruler and compasses.\"}]","Introduction to Abstract Algebra - Introduction | PDF",252]