Ring theory

Instructor: Vera Serganova
Email address: serganov@math webpage:/~serganov Phone Number: 642-2150
  • Office hours: Tu 12:30-1:30, Th 5:00-6:00 in 709 Evans
  • Text: T. Y. Lam A first Course in Noncommutative rings
  • Homework: Every Tuesday a problem assignment will be posted on this page. The homework will be collected the following Tuesday.
  • Grading policy: 70% homework, 30% take-home final exam
  • Announcement: No class on Tuesday 9/27
  • Topics
  • Artinian and Noetherian rings and modules
  • Semisimple rings. Wedderburn-Artin theory
  • The Jacobson radical
  • Modules over finite-dimensional algebras. Groups and quivers.
  • Prime and primitive rings
  • Division rings
  • Local and semilocal rings. Idempotents and block decomposition
  • Perfect and semiperfect rings
  • Projective and injective modules
  • Quadratic rings and Koszul rings(if time permits)
  • Morita equivalence (if time permits)
  • Problem set #1.
  • Problem set #2.
  • Problem set #3.
  • Problem set #4.
  • Problem set #5.
  • Problem set #6.
  • Problem set #7.
  • Problem set #8.
  • Problem set #9.
  • Problem set #10.
  • Problem set #11.
  • Lecture notes (draft of the book).
  • Final exam. Due 12/9.