Abstract Algebra

Lessons

What is Abstract Algebra?
Group Definition
Group Definition (Quick)
Cosets and Lagrange's Theorem
Cayley Tables
Groups - Motivation for Definition
Normal Subgroups and Factor Groups
Subgroups
Cyclic Groups
Group or Not Group? (Integer Edition)
Group Homomorphisms
Group Homomorphisms (Quick)
Isomorphisms for Groups
Kernel of Group Homomorphisms
Order of an Element
Cycle Notation for Permutations
Symmetric Groups
Dihedral Groups
Direct Products of Groups
Matrix Groups
Simple Groups
Symmetry Groups of Triangles
Ring Definition
Ring Definition (Quick)
Ring Examples
Units in a Ring
Field Definition
Field Definition (Quick)
Field Examples: Infinite Fields
Ideals in Rings
Integral Domains
Modules
Vector Spaces

Group Homomorphisms

A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be used through abstract algebra. You will study homomorphisms between groups, rings, fields, modules, vector spaces, and more.

A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be used through abstract algebra. You will study homomorphisms between groups, rings, fields, modules, vector spaces, and more.

Course Page
Abstract Algebra

Resources

Abstract Algebra Textbook
Abstract Algebra Textbook
Abstract Algebra by Dummit & Foote is a standard textbook used by colleges and universities. It is extremely well written with lots of examples and exercises. It covers all the topics for a solid first course in Abstract Algebra. We use this on occasion as a reference for inspiration or reference. Highly recommended!
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