Selected exercises in algebra. Volume 1 (2020)

• Record Type: Book
• Uniform Title: Esercizi Scelti ai Algebra.
• Further Information: Note: Rocco Chirvì, Ilaria Del Corso, Roberto Dvornicich.
• Other Names: Chirvì, Rocco; Del Corso, Ilaria; Dvornicich, Roberto
• Contents: Intro -- Preface -- Preface to the English Edition -- Contents -- 1 Theory -- 1 Fundamentals -- 1.1 Sets -- 1.2 Maps -- 1.3 Relations -- 1.4 The Principle of Induction -- 1.5 Operations -- 1.6 Numbers -- 2 Combinatorics -- 3 Integers -- 3.1 Divisibility of Integers -- 3.2 Congruences -- 3.3 Modular Arithmetic -- 4 Groups -- 4.1 Definition and Basic Properties -- 4.2 Subgroups -- 4.3 Product of Subgroups -- 4.4 Cosets of a Subgroup -- 4.5 Normal Subgroups -- 4.6 The Symmetric Group -- 4.7 Group Homomorphisms -- 4.8 Direct Product of Groups -- 5 Rings -- 5.1 Definition and Basic Properties 5.2 Subrings, Ideals and Quotients -- 5.3 Polynomial Rings -- 5.4 Divisibility of Polynomials -- 5.5 Polynomial Factorisation -- 5.6 Quotients of Polynomial Rings -- 6 Fields -- 6.1 Characteristic of a Field -- 6.2 Multiplicative Group -- 6.3 Field Extensions -- 6.4 Splitting Field -- 6.5 Finite Fields -- 7 Preliminary Exercises -- 2 Exercises -- 1 Sequences -- 2 Combinatorics -- 3 Congruences -- 4 Groups -- 5 Rings and Fields -- 3 Solutions -- 1 Sequences -- 2 Combinatorics -- 3 Congruences -- 4 Groups -- 5 Rings and Fields -- Index
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 512; Algebra -- Problems, exercises, etc; Algebra; Electronic books; Problems and exercises
• Languages: English
• ISBNs: 9783030361563
• Related ISBNs: 303036156X; 3030361551; 9783030361556
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.