Felix Gotti

Here is a link to some of the most recent courses I have taught.

Ideal Theory and Prüfer Domains (MIT, IAP 2021)

Hours: Mondays/Wednesdays/Fridays 4-5pm (via Zoom)

Textbook: We will follow the structure of Gilmer's book "Multiplicative Ideal Theory"

Lecture Notes

• Preliminaries on Rings and Modules
  
  
• Lecture 1: Localization
• Lecture 2: Prime and Maximal Ideals
• Lecture 3: Radical and Primary Ideals
• Lecture 4: Primary Decompositions
• Lecture 5: One-dimensional Noetherian Rings
• Lecture 6: Krull's Theorems
• Lecture 7: Integral Extensions I (Basic Properties)
• Lecture 8: Integral Extensions II (Spectral Theorems)
• Lecture 9: Fractional Ideals
• Lecture 10: Valuation Domains I (Characterizations)
• Lecture 11: Valuation Domains II (Overrings and Integral Closures)
• Lecture 12: Discrete Valuation Rings
• Lecture 13: Dedekind Domains
• Lecture 14: Prüfer Domains I (Characterizations)
• Lecture 15: Prüfer Domains II (Overrings)
• Lecture 16: Almost Dedekind Domains
• Lecture 17: Integer-Valued Polynomials I (The Spectrum)
• Lecture 18: Integer-Valued Polynomials II (Prüferness)