MATH:5010 - Spring 2017
Homework
Assignment 7
Reading (from Dummit and Foote AND Lang's "Algebra" book):
Read Sections 12.3, 13.1, 13.2, 13.4 from Dummit and Foote.
Also read Sections V.1, V.2 from Lang (Chapters V and VI are posted on ICON on the MATH:5010:0AAA site in "Modules")
Please look through the sections for EACH lecture before the lecture.
See the Lecture Schedule for the sections that will be covered.
Then after EACH lecture, review your lecture notes and
thoroughly read the sections covered in class.
Part A Problems (to be handed in on
Tuesday, March 21, at the beginning of the discussion section):
- Section 12.3: # 26.
IMPORTANT for #26: p is a prime number. One way of doing this problem is
to bring xI-A into its Smith normal form (look at n=2 and n=3 to see what to do for
general n).
- Section 13.2: # 8, 14, 16.
IMPORTANT for #14: F is a field, α is algebraic over F.
Part B Problems (to be handed in on
Friday, March 24, at the beginning of the lecture):
If you hand in ALL Part B Problems together with the Part A Problems already on
Tuesday, March 21, 2 extra points will be added to your homework score.
- Section 12.3: # 30.
IMPORTANT: Assume all eigenvalues of T lie in F.
- Section 13.2: # 9, 15, 17.
IMPORTANT for #15: The degree of α is the degree [F(α):F]
when they talk of a counterexample of minimal degree.
Additional Practice Problems (you have
to know how to do these, but you do NOT have to hand these in):
- Section 12.3: # 24, 25, 27, 28, 32, 33, 34,
37, 38, 39.
- Section 13.1: # 1, 2, 3, 7, 8.
- Section 13.2: # 3, 4, 5, 6, 7, 10, 11, 12, 13.
Frauke Bleher
Mar 07 2017