Assignment 1, due January 14:
Section 10.4: 4, 5, 7, 10, 12, 17, 18, 19, 25, 27
Assignment 2, due Wednesday January 23:
Section 11.5: 1, 2, 8, 9, 13; Section 10.5: 1
(10.5: 4, 16, 18 will be on next problem set!)
Assignment 3, due January 28:
10.5: 4, 9, 13, 15, 16, 18, 20, 22, 24
In Exercise 15(a), you need not assume M is an R-module.
It suffices that M be an abelian group.
No office hours January 28 or 30, but our course assistant Matt Simpson will be available Monday at noon in HB39.
Assignment 4, due February 4:
Section 9.6: 2, 10, 11, 12, 24, 32(note: see #5), 34, 35, 40, 42
Assignment 5, due February 11:
Section 15.1: 10, 16, 23, 41, 42, 43, 48; Section 15.2: 3, 4, 8
Assignment 6, due February 18:
Section 15.2: 13, 17, 21, 31, 33, 34, 41, 50; Section 15.3: 4, 5
Extra credit: Find a counterexample to Problem 13 when k is not
algebraically closed!
(Even if V is Zariski disconnected, we might not
have a direct sum decomposition for k[V].)
Assignment 7, due March 10:
Section 15.3: 7, 10, 11, 20, 26, 27; Section 15.4: 13, 14, 15, 16
Assignment 8, due March 17:
Section 15.4: 25, 26, 27; Section 15.5: 10, 14, 15, 16, 31
Assignment 9, due March 23:
Section 16.1: 4, 8, 9, 13, 14; Section 16.2: 1, 3, 8, 9
In problem 16.1.9, J denotes the Jacobson radical.
No office hours March 21, but our course assistant Matt Simpson will be available Friday at 3PM in HB39.
Assignment 10, due March 30:
Section 16.3: 14, 16, 17, 21, 22, 24;
Section 17.1: 3, 4, 7
For problem 17(b), define the product by [I][J]=[IJ].
Assignment 11, due April 7:
Section 17.1: 8 (if you haven't done it already), 10abc,
17, 19ab, 26, 31, 32
It looks like Problem 32 might be wrong--details to come.
Assignment
12, due April 14:
Assignment 13, due April 23:
Office hours: Tuesday, April 22, 1-2:30