An Introduction to Abstract Algebra/李晓培段樱桃/复旦大学出版社


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	An Introduction to Abstract Algebra
	作者：	李晓培段樱桃
	定价：	28 元	页数：	139页
	ISBN：	978-7-309-08368-2/O.475	字数：	158千字
	开本：	16 开	装帧：	平装
	出版日期：	2011年8月	本类其他相关图书
内容提要
TheoriginsofalgebracanbetracedbacktoMuhammadbenMusaal-Khwarizmi,whoworkedatthecourtoftheCaliphal-Ma’muninBaghdadintheearly9thcentury.ThewordofalgebracomesfromtheArabical-jabr,whichreferstotheprocessofaddingthesamequantitytobothsidesofanequation. Abstractalgebraisthesubjectareaofmathematicsthatstudiesfundamentalalgebraicstructures,namelygroups,rings,fieldsetc..Thetechniquesareusedinmanyareasofmathematics,andthereareapplicationstophysics,engineeringandcomputerscienceaswell.Thephraseabstractalgebrawascoinedattheturnofthe20thcenturytodistinguishthisareafromwhatwasnormallyreferredtoasalgebra,thestudyoftherulesformanipulatingformulaeandalgebraicexpressionsinvolvingunknownsandrealorcomplexnumbers,oftennowcalledelementaryalgebra.Thedistinctionisrarelymadeinmorerecentwritings. Thisbookmainlyfocusonthetheoryofgroups,ringsandfieldsandcanbeusedasatextbookfortheundergraduatestudents.Toaccommodatethereadershavingdifferentbackground,thefirstchapterpresentsthepreliminarieswhichcanhelpthebeginnerstobefamiliarwithseveralconceptssuchasset, subset, operationsonsets,function, equivalencerelationshipsandpartitionofsets.Chaptertwoisanintroductiontogrouptheory,includingsubgroups, cyclegroup,symmetricgroup,normalsubgroup, quotientgroup,p-group,simplegroupandsolvablegroup.Moreover,severalwellknowntheoremssuchasLagrangestheorem,Cauchystheorem,Sylowtheoremarealsointroduced.Chapterthreeisanintroductiontoringsandfields.Inthischapter,firstlythedefinitionsandelementarypropertiesofrings,subringsandideals,ringhomomorphisms,polynomialsringsaregiven,thenfurther,fromthepolynomialstofieldsanduniquefactorizationdomainsarestudied.Thefirsttwochapters,whichcontainmuchelementarymaterial,areagoodplaceforthereadertodevelopandpolishtheskillstoprovetheoremsprovingskills.Eachsectionofthebookisfollowedbyaselectionofproblems,ofvaryingdegreesofdifficulty. TheauthorsareamgratefultoprofessorJiaLiPingformuchgoodadviceandlotsofstimulatingconversationswhichhaveledtonumerousimprovementsinthetextbook.InparticularWearemostgratefultoYanniChenandtherefereesforhervaluablecommentsandmanyconstructivesuggestionswhichgreatlyimprovedourpresentation.Finally,wethankprofessorDonforhisencouragementandunfailingcourtesyandassistance.
作者简介
李晓培，男，四川成都人，生于1966年10月，中共党员，理学博士，数学教授。湛江师范学院数学与计算科学学院院长。现主要研究方向是：微分方程与动力系统。段樱桃，女，陕西西安人，1972年10月生，中共党员，理学硕士，讲师。湛江师范学院数学与计算科学学院教师。主要研究方向：算子理论与小波分析。
书摘
Chapter 1 Preliminaries 1.1 Sets, Subsets and Operations on Sets 1.2 Functions 1.3 Equivalence Relations and the Partition of Sets Exercises Chapter 2 Groups 2.1 Binary Operation 2.2 Definitions and Examples for a Group 2.3 Elementary Properties of Groups 2.4 Subgroups 2.5 Cyclic Group 2.6 Symmetric Group 2.7 Cosets and Lagrange’s Theorem 2.8 Normal Subgroups and Quotient Groups 2.9 Homomorphisms 2.10 The Structure of p-Groups 2.11 The Sylow Theorems 2.12 Simple Group 2.13 Solvable Groups Exercises Chapter 3 Rings and Fields 3.1 Definition and Elementary Properties of Rings 3.2 Subrings and Ideals 3.3 Ring Homomorphisms 3.4 Polynomials Rings 3.5 From Polynomials to Fields 3.6 Unique Factorization Domains Exercises 附录数学英语词汇 Bibliography
书评



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