Selected Exercises in Algebra : Volume 2

Selected Exercises in Algebra : Volume 2

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Bibliographic Details
Main Author: Chirivì, Rocco
Other Authors: Caraceni, Alessandra, Del Corso, Ilaria, Dvornicich, Roberto
Format: Book
Language:English
Published: Cham : Springer International Publishing AG, 2023
Series:Unitext Ser
Table of Contents:
  • 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

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