In this program
- Rings: definitions and examples (Z, polynomial rings, matrix rings)
- Integral domains, fields, and ideals
- Quotient rings and ring homomorphisms
- Polynomial rings
- Field extensions
- Constructibility (introduction)
Rings and fields
Rings: definitions and examples (Z, polynomial rings, matrix rings)
Abstract algebra · Theoretical / proof-based
Topic
Rings: definitions and examples (Z, polynomial rings, matrix rings)
Undergraduate Abstract Algebra — scope drawn from open algebra texts (e.g. Judson Abstract Algebra: Theory and Applications, AIM-approved) and typical US undergraduate algebra syllabi.