18.706 Noncommutative Algebra.(Fall 2020)
MW 11:00am-12:30pm (US eastern time)
Zoom meeting ID: 949 4570 2542 (registration and passcode required, passcode will be sent to the class by email)
TA: Timothy Ngotiaoco
Office hours: Ngotiaoco, Tuesdays 1pm-2pm; Yun, Tuesdays 9:30pm-10:30pm; Both office hours use Zoom ID: 917 0098 1657
Homework (due by 11:59pm on the date specified below)
HW10: pdf, tex, due on Nov. 18
Lecture notes
Lecture 1 (9/2): Examples of rings. Notes
Lecture 2 (9/9): More examples of rings. Modules. Notes
Lecture 3 (9/14): Jordan-Holder theorem. Semisimple modules. Notes
Lecture 4 (9/16): Semisimple rings. Wedderburn's theorem. Density theorem. Primitive rings. Notes
Lecture 5 (9/21): Simple rings. Artinian and Noetherian. Wedderburn-Artin theorem. Notes
Lecture 6 (9/23): Jacobson radical. Hopkin-Levetzki theorem. Notes
Lecture 7 (9/28): More on Jacobson radical. Nakayama's lemma. Notes
Lecture 8 (9/30): Quivers and path algebras. Group rings. Notes
Lecture 9 (10/5): Characters. Indecomposable modules. Notes
Lecture 10 (10/7): Krull-Schmidt theorem. Projective modules. Notes
Lecture 11 (10/13): Projective covers. Notes
Lecture 12 (10/14): Injective modules. Notes
Lecture 13 (10/19): Injective hulls. Category theory. Notes
Lecture 14 (10/21): Notes
Lecture 15 (10/26): Notes
Lecture 16 (10/28): Notes
Lecture 17 (11/2): Notes
Lecture 18 (11/4): Notes
Lecture 19 (11/9): Notes
Lecture 20 (11/16): Notes
Lecture 21 (11/18): Notes
Lecture 22 (11/30): Notes
Lecture 23 (12/2): Notes
Lecture 24 (12/7): Notes
Lecture 25 (12/9): Notes
References:
Mike Artin's notes
P.M. Cohn, Further Algebra and Applications. Chapters 2, 4, 5, 7, 8.
T.Y.Lam, A First Course in Noncommutative Rings (GTM 131). Chapters 1,2,3,4,5.
T.Y.Lam, Lectures on Modules and Rings. (GTM 189). Chapters 1,4,7.