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MAT 3143

Rings and Modules

3 units

Fall 2020

Topics

  • Rings, ideals, quotient rings and homomorphisms
  • Isomorphism results and the Chinese remainder theorem
  • Polynomial rings, irreducibility and factorization
  • Construction of finite fields
  • Unique factorization, principal ideal and Euclidean domains
  • Modules, direct sums, annihilators and free modules
  • Classification over principal ideal domains

Readings

  • Abstract Algebra: Theory and Applications
    Thomas W. Judson · Open course text
  • Algebra: Abstract and Concrete
    Frederick M. Goodman · Text used for selected later topics
  • MAT3143-Rings and Modules ↗
    Lecture notes / supplementary course reference
Sources