ALGEBRA 612. HOMEWORK 8.
DUE BEFORE THE DISCUSSION SECTION ON APRIL 10.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make s
ALGEBRA 612. MIDTERM I. SOLUTIONS.
1. Let L/K be a nite Galois extension with Galois group G. A map
f : G L is called a Galois 1-cocycle if it has the following property:
f ( ) = f ()(f ( )
for any
, G.
L
Show that a map f : G
is a Galois 1-cocycle if an
ALGEBRA 612. MIDTERM 2 SOLUTIONS.
1. Let A B be rings such that B is integral over A. Let f : A C be
any homomorphism. Show that there exists a homomorphism g : B C
such that g|A = f .
Proof. Let q A be the kernel of f . Since the image of f is a domain D
ALGEBRA 612. HOMEWORK 1. DUE BEFORE CLASS OR
DISCUSSION SECTION ON FEB 5.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make
ALGEBRA 612. HOMEWORK 4. DUE BEFORE CLASS ON FEB 26
OR DISCUSSION SECTION ON FEB 27.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem.
ALGEBRA 612. HOMEWORK 5. DUE BEFORE THE DISCUSSION
SECTION ON MAR 6.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sure
ALGEBRA 612. HOMEWORK 3. DUE BEFORE CLASS ON FEB 19
OR DISCUSSION SECTION ON FEB 20.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem.
ALGEBRA 612. HOMEWORK 2. DUE BEFORE CLASS ON FEB 12
OR DISCUSSION SECTION ON FEB 13.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem.
ALGEBRA 612. HOMEWORK 9.
DUE BEFORE THE DISCUSSION SECTION ON APRIL 24.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make s
ALGEBRA 612. HOMEWORK 6.
DUE BEFORE THE DISCUSSION SECTION ON MAR 27.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sur
ALGEBRA 612. HOMEWORK 10.
DUE BEFORE THE DISCUSSION SECTION ON MAY 1.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sur
ALGEBRA 612. HOMEWORK 7.
DUE BEFORE CLASS ON APRIL 4.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sure that all solut
ALGEBRA 612. FINAL EXAM.
The test contains nine problems but you have to select only ve of them,
including at least one from each of the rst two sections and at least two
from the last section. Only these ve problems will be graded. Each problem is worth