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Introduction to Algebraic Structures
An algebraic structure is a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms. Examples of algebraic structures include groups, rings, fields, and lattices.
- Author
- Tom Denton
- Publisher
- Google Research
- Source
- LibreTexts
- Language
- EN
- Category
- Basic Sciences
Contents· 38 sections
- 01: Symmetry
- 1.01: Symmetry
- 1.02: Counting Symmetries
- 1.03: Symmetric Polynomials
- 1.04: Abstraction. What is a group?
- 02: Groups I
- 2.01: Symmetry and Functions
- 2.02: Definition of a Group
- 2.03: Integers Modulo n
- 2.04: Permutations
- 03: Groups II
- 3.01: Generating Sets
- 3.02: Visualizing Groups- Cayley Graphs
- 3.03: Subgroups
- 3.04: Cosets and Lagrage's Theorem
- 04: Groups III
- 4.01: Homomorphisms
- 4.02: Product Groups
- 4.03: Image and Kernel
- 05: Groups IV
- 5.01: Quotient Groups
- 5.02: Examples of Quotient Groups
- 5.03: Isomorphism Theorem
- 5.04: Classifying Finite Groups
- 06: Group Actions
- 6.01: Group Actions
- 6.02: Orbits and Stabilizers
- 6.03: Counting
- 07: Rings I
- 7.01: Juggling With Two Operations
- 7.02: Ring Homomorphisms
- 08: Rings II
- 8.01: The Problem of Division
- 8.02: Field of Fractions
- 8.03: Euclidean Domains
- 09: Vector Spaces
- 9.01: A Return to Linear Algebra
- 9.02: Linear Independence