Math 4123A/9023A: Rings and Modules

• Instructor: S. Rankin, Middlesex College 132.

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• Office hours policy: drop in any time except Mon-Wed afternoon. If you wish to arrange a specific time to meet, or just to discuss a problem, email is a good way to communicate with me.
• Course Outline.

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• Presentations:
  • 1. Tuesday, Dec 6 MC 107 11:00-12:00 Banhita (existence and uniqueness of finite fields).
  • 2. Tuesday, Dec 6 MC 108 1:30-2:30 Ben (integral extensions, and the ring of integers of a quadratic extension of the rationals).
  • 3. Tuesday, Dec 6 MC 107 5:30-6:30 Mohammed (Category theory).
  • 4. Wednesday, Dec 7 MC 107 5:00-6:00 Sujanthan (Artinian rings\).
  • 5. Thursday, Dec 8 MC 106 1:00-2:00 Hanyuan (Discrete Valuation Rings).
  • 6. Thursday, Dec 8 MC 108 3:00-4:00 Brett (Completions of Rings).
  • 7. Thursday, Dec 8 MC 107 5:00-6:00 Girish (Noetherian Rings).
  • 8. Friday, Dec 9 MC 107 12:30-1:30 Majed (Radicals of Ideals in Noetherian Rings).
  • 9. Friday, Dec 9 MC 107 2:00-3:00 Barum (Hilbert's Nullstellensatz).
  • 10. Friday, Dec 9 MC 107 3:30-4:30 Chandra (Prime Spectrum of a Ring)
• Bulletin Board
  • Correction to question 4 on the final: make R commutative as well.
  • Notes on the classification of finitely generated modules over a PID.
  • The take-home final exam is now posted. It is due Monday, December 12, 2011.
  • The solutions for Assignment 4 are now posted.
  • Irreducibility of the cyclotomic polynomials in Z[x].
  • Here is the proof that each finite subgroup of the multiplicative group of a field is cyclic.
  • Here are the notes on the irreducibility of x^4+1 in Z[x] and Z/(4)[x], and the reducibility in Z/(p)[x] for all primes p.
  • The solutions for the midterm are now posted.
  • Notes on the proof that if R is a UFD, then R[x] is a UFD.
  • Notes on the proof that every PID is UFD.
  • The solutions for Assignment 3 are now posted.
  • The solutions for Assignment 2 are now available.
  • Here is a write-up establishing the equivalence of Zorn's Lemma and the Axiom of Choice.
  • The solutions for Assignment 1 are now posted.

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