Math 831 ABSTRACT ALGEBRA II
QUIZ III REVISED
March 6 (Fri), 2009
Due date: March 16 (Mon), 2009
Instructor:
Yasuyuki Kachi
Line #: 82255.
ID :
[I] (40pts)
Name :
We work over the polynomial ring C x . Use the notion of resultants
covered in class 03/06/0
Math 831 ABSTRACT ALGEBRA II
QUIZ II
February 18 (Wed), 2009
Yasuyuki Kachi
Instructor:
Line #: 82255.
ID :
[I] (20pts)
Name :
Let
1 = x + y + z ,
2 = x y + y z + z x,
3 = x y z .
Agree that we have
x2 + y 2 + z 2 = 1 2 2 2 ,
and
x3 + y 3 + z 3 = 1 3 3 1
Math 831 ABSTRACT ALGEBRA II
QUIZ I
February 16 (Mon), 2009
Yasuyuki Kachi
Instructor:
Line #: 82255.
Name :
ID :
[I] (110pts)
x
f y
z
Let
=
x+y+z
xy + yz + zx ,
xyz
x
z =
f
y
(1)
.
y
z =
f
x
(2)
f 1
(3)
f 1
regarded as
f : C3
C3 .
a mapping
(4)
.
Math 831 ABSTRACT ALGEBRA II
HINTS FOR HOMEWORK III
February 6 (Fri), 2009
Yasuyuki Kachi
Instructor:
Line #: 82255.
Homework set III:
The following problems from Progress Check I:
The following problems from Progress Check I, 1:
Problem [XVI] page 27 ,
Math 831 ABSTRACT ALGEBRA II
SOLUTION FOR HOMEWORK II
February 2 (Mon), 2009
Yasuyuki Kachi
Instructor:
Line #: 82255.
Homework set II
Due Monday, February 2nd, 2009 .
The following problems from Progress Check I, 1:
Problem [IX] page 19 ,
Problem [X] p
Math 831 ABSTRACT ALGEBRA II
HINTS FOR HOMEWORK I
January 24 (Sat), 2009
Instructor:
Yasuyuki Kachi
Line #: 82255.
Homework set I:
The following problems from Progress Check I:
Problem [IV] page 13 ,
Problem [V] page 13 ,
Problem [VI] page 14 ,
Problem [
Math 831 ABSTRACT ALGEBRA II
SOLUTION FOR MIDTERM EXAM I
March 23 (Mon), 2009
Instructor:
Yasuyuki Kachi
Line #: 82255.
[I] (25pts)
Let
Z
1
=
m+
Find one pair of complex numbers
2 + 2 = 1,
Z
1 ,
(i)
(ii)
1 n C
,
2 Z
m, n Z
C2 such that
3 Z
1 ,
1 ,
and