Abstract Algebra: Structures
Before this course
Modular arithmetic, functions and proof methods.
Review a prerequisite lesson →- 01Groups, Subgroups & Cosets
Use a concrete cyclic group to distinguish elements, subgroup size and the number of cosets.
- 02Homomorphisms, Kernels & Images
Check preservation of operations and connect kernel and image sizes for finite groups.
- 03Rings, Ideals & Fields
Distinguish additive inverses from multiplicative inverses and test modular examples for field behavior.
After these topics
General quotient constructions, isomorphism theorems, ideals, field extensions and proof practice.
The topics above describe this library’s current scope, not a complete university course. Use the reference readings and written exercises to continue.