02721nam 2200493 450 991063392030332120230512093259.03-031-12651-3(MiAaPQ)EBC7148645(Au-PeEL)EBL7148645(CKB)25504436200041(PPN)266349455(EXLCZ)992550443620004120230413d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierSelected exercises in algebraVolume 2 /Rocco Chirivì, Ilaria Del Corso, Roberto DvornicichCham, Switzerland :Springer,[2022]©20221 online resource (301 pages)Unitext - Matematica per il 3 + 2 ;Volume 140Includes index.Print version: Chirivì, Rocco Selected Exercises in Algebra Cham : Springer International Publishing AG,c2023 9783031126505 Intro -- Preface -- Contents -- 1 Theory -- 1.1 Groups -- 1.1.1 Basic Notions -- 1.1.2 Homomorphism Theorems -- 1.1.3 Free Groups -- 1.1.4 Presentations of Groups -- 1.1.5 The Dihedral Group -- 1.1.6 Group Automorphisms -- 1.1.7 Commutators and Abelianisation -- 1.1.8 Group Actions -- 1.1.9 The Action by Conjugation -- 1.1.10 The Action by Multiplication -- 1.1.11 p-Groups -- 1.1.12 Permutations -- 1.1.13 Abelian Groups -- 1.1.14 Semidirect Product -- 1.1.15 Sylow Theorems -- 1.1.16 Simple Groups -- 1.2 Rings -- 1.2.1 Basic Notions -- 1.2.2 Maximal and Prime Ideals -- 1.2.3 Quotient Rings -- 1.2.4 Ideal Operations -- 1.2.5 Fraction Fields and Localisations -- 1.2.6 Divisibility -- 1.2.7 Euclidean Domains -- 1.2.8 Principal Ideal Domains -- 1.2.9 Unique Factorisation Domains -- 1.2.10 Gaussian Integers -- 1.3 Fields and Galois Theory -- 1.3.1 Basic Notions -- 1.3.2 Homomorphism Extensions -- 1.3.3 Galois Correspondence -- 1.3.4 Cyclotomic Extensions -- 1.3.5 Straightedge and Compass Constructions -- 1.4 Preliminary Exercises -- 2 Exercises -- 2.1 Groups -- 2.2 Rings -- 2.3 Fields and Galois Theory -- 3 Solutions -- 3.1 Groups -- 3.2 Rings -- 3.3 Fields and Galois theory -- Index.Unitext.Matematica per il 3+2 ;Volume 140.AlgebraÀlgebrathubLlibres electrònicsthubAlgebra.Àlgebra512.9Chirivì Rocco767331Del Corso IlariaDvornicich RobertoMiAaPQMiAaPQMiAaPQBOOK9910633920303321Selected Exercises in Algebra2161932UNINA