eBook - PDF
An Introduction to Abstract Algebra
Derek J. S. Robinson
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- 292 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
An Introduction to Abstract Algebra
Derek J. S. Robinson
Book details
Table of contents
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Topic
MathématiquesSubtopic
Algèbre abstraiteTable of contents
- 1 Sets, relations and functions
- 1.1 Sets and subsets
- 1.2 Relations, equivalence relations and partial orders
- 1.3 Functions
- 1.4 Cardinality
- 2 The integers
- 2.1 Well-ordering and mathematical induction
- 2.2 Division in the integers
- 2.3 Congruences
- 3 Introduction to groups
- 3.1 Permutations of a set
- 3.2 Binary operations: semigroups, monoids and groups
- 3.3 Groups and subgroups
- 4 Cosets, quotient groups and homomorphisms
- 4.1 Cosets and Lagrange’s Theorem
- 4.2 Normal subgroups and quotient groups
- 4.3 Homomorphisms of groups
- 5 Groups acting on sets
- 5.1 Group actions and permutation representations
- 5.2 Orbits and stabilizers
- 5.3 Applications to the structure of groups
- 5.4 Applications to combinatorics – counting labellings and graphs
- 6 Introduction to rings
- 6.1 Definition and elementary properties of rings
- 6.2 Subrings and ideals
- 6.3 Integral domains, division rings and fields
- 7 Division in rings
- 7.1 Euclidean domains
- 7.2 Principal ideal domains
- 7.3 Unique factorization in integral domains
- 7.4 Roots of polynomials and splitting fields
- 8 Vector spaces
- 8.1 Vector spaces and subspaces
- 8.2 Linear independence, basis and dimension
- 8.3 Linear mappings
- 8.4 Orthogonality in vector spaces
- 9 The structure of groups
- 9.1 The Jordan-Holder Theorem
- 9.2 Solvable and nilpotent groups
- 9.3 Theorems on finite solvable groups
- 10 Introduction to the theory of fields
- 10.1 Field extensions
- 10.2 Constructions with ruler and compass
- 10.3 Finite fields
- 10.4 Applications to latin squares and Steiner triple systems
- 11 Galois theory
- 11.1 Normal and separable extensions
- 11.2 Automorphisms of field extensions
- 11.3 The Fundamental Theorem of Galois Theory
- 11.4 Solvability of equations by radicals
- 12 Further topics
- 12.1 Zorn’s Lemma and its applications
- 12.2 More on roots of polynomials
- 12.3 Generators and relations for groups
- 12.4 An introduction to error correcting codes
- Bibliography
- Index of notation
- Index