LEADER 02721nam 2200493 450 001 9910633920303321 005 20230512093259.0 010 $a3-031-12651-3 035 $a(MiAaPQ)EBC7148645 035 $a(Au-PeEL)EBL7148645 035 $a(CKB)25504436200041 035 $a(PPN)266349455 035 $a(EXLCZ)9925504436200041 100 $a20230413d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSelected exercises in algebra$hVolume 2 /$fRocco Chirivi?, Ilaria Del Corso, Roberto Dvornicich 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (301 pages) 225 1 $aUnitext - Matematica per il 3 + 2 ;$vVolume 140 300 $aIncludes index. 311 08$aPrint version: Chirivì, Rocco Selected Exercises in Algebra Cham : Springer International Publishing AG,c2023 9783031126505 327 $aIntro -- Preface -- Contents -- 1 Theory -- 1.1 Groups -- 1.1.1 Basic Notions -- 1.1.2 Homomorphism Theorems -- 1.1.3 Free Groups -- 1.1.4 Presentations of Groups -- 1.1.5 The Dihedral Group -- 1.1.6 Group Automorphisms -- 1.1.7 Commutators and Abelianisation -- 1.1.8 Group Actions -- 1.1.9 The Action by Conjugation -- 1.1.10 The Action by Multiplication -- 1.1.11 p-Groups -- 1.1.12 Permutations -- 1.1.13 Abelian Groups -- 1.1.14 Semidirect Product -- 1.1.15 Sylow Theorems -- 1.1.16 Simple Groups -- 1.2 Rings -- 1.2.1 Basic Notions -- 1.2.2 Maximal and Prime Ideals -- 1.2.3 Quotient Rings -- 1.2.4 Ideal Operations -- 1.2.5 Fraction Fields and Localisations -- 1.2.6 Divisibility -- 1.2.7 Euclidean Domains -- 1.2.8 Principal Ideal Domains -- 1.2.9 Unique Factorisation Domains -- 1.2.10 Gaussian Integers -- 1.3 Fields and Galois Theory -- 1.3.1 Basic Notions -- 1.3.2 Homomorphism Extensions -- 1.3.3 Galois Correspondence -- 1.3.4 Cyclotomic Extensions -- 1.3.5 Straightedge and Compass Constructions -- 1.4 Preliminary Exercises -- 2 Exercises -- 2.1 Groups -- 2.2 Rings -- 2.3 Fields and Galois Theory -- 3 Solutions -- 3.1 Groups -- 3.2 Rings -- 3.3 Fields and Galois theory -- Index. 410 0$aUnitext.$pMatematica per il 3+2 ;$vVolume 140. 606 $aAlgebra 606 $aÀlgebra$2thub 608 $aLlibres electrònics$2thub 615 0$aAlgebra. 615 7$aÀlgebra 676 $a512.9 700 $aChirivi?$b Rocco$0767331 702 $aDel Corso$b Ilaria 702 $aDvornicich$b Roberto 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910633920303321 996 $aSelected Exercises in Algebra$92161932 997 $aUNINA