03639nam 2200589 450 991080714630332120230807212114.01-118-49775-91-118-49776-7(CKB)3710000000277344(EBL)1834778(SSID)ssj0001412632(PQKBManifestationID)11807981(PQKBTitleCode)TC0001412632(PQKBWorkID)11415157(PQKB)11486178(MiAaPQ)EBC1834778(DLC) 2014023084(Au-PeEL)EBL1834778(CaPaEBR)ebr10976521(OCoLC)895431394(EXLCZ)99371000000027734420141118h20152015 uy 0engur|n|---|||||txtccrAn introduction to essential algebraic structures /Martyn R. Dixon, Leonid A. Kurdachenko, Igor Ya. SubbotinHoboken, New Jersey :Wiley,2015.©20151 online resource (243 p.)Includes index.1-118-45982-2 Includes bibliographical references and index.An Introduction to Essential Algebraic Structures; Copyright; Contents; Preface; Chapter 1 Sets; 1.1 Operations on Sets; Exercise Set 1.1; 1.2 Set Mappings; Exercise Set 1.2; 1.3 Products of Mappings and Permutations; Exercise Set 1.3; 1.4 Operations on Matrices; Exercise Set 1.4; 1.5 Binary Algebraic Operations and Equivalence Relations; Exercise Set 1.5; Chapter 2 Numbers; 2.1 Some Properties of Integers: Mathematical Induction; Exercise Set 2.1; 2.2 Divisibility; Exercise Set 2.2; 2.3 Prime Factorization: The Fundamental Theorem of Arithmetic; Exercise Set 2.32.4 Rational Numbers, Irrational Numbers, and Real NumbersExercise Set 2.4; Chapter 3 Groups; 3.1 Groups and Subgroups; Exercise Set 3.1; 3.2 Cosets and Normal Subgroups; Exercise Set 3.2; 3.3 Factor Groups and Homomorphisms; Exercise Set 3.3; Chapter 4 Rings; 4.1 Rings, Subrings, Associative Rings; Exercise Set 4.1; 4.2 Rings of Polynomials; Exercise Set 4.2; 4.3 Ideals and Quotient Rings; Exercise Set 4.3; 4.4 Homomorphisms of Rings; Exercise Set 4.4; Chapter 5 Fields; 5.1 Fields: Basic Properties and Examples; Exercise Set 5.1; 5.2 Some Field Extensions; Exercise Set 5.25.3 Fields of Algebraic NumbersExercise Set 5.3; Hints and Answers to Selected Exercises; Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Index; End User License Agreement A reader-friendly introduction to modern algebra with important examples from various areas of mathematicsFeaturing a clear and concise approach, An Introduction to Essential Algebraic Structures presents an integrated approach to basic concepts of modern algebra and highlights topics that play a central role in various branches of mathematics. The authors discuss key topics of abstract and modern algebra including sets, number systems, groups, rings, and fields. The book begins with an exposition of the elements of set theory and moves on to cover the main ideas and branches of abstract algeOrdered algebraic structuresOrdered algebraic structures.511.3/3Dixon Martyn R(Martyn Russell),1955-62617Kurdachenko Leonid A.1949-Subbotin Igor Ya.1950-MiAaPQMiAaPQMiAaPQBOOK9910807146303321An introduction to essential algebraic structures3951980UNINA