Algebra Qualifying Examination
January 2002
Directions:
1. Answer all questions. (Total possible is 100 points.)
2. Start each question on a new sheet of paper.
3. Write only on one side of each sheet of paper.
Policy on Misprints:
The Qualifying Exam Committee tries to proofread the exams as carefully as possible. Nevertheless,
the exam may contain a few misprints. If you are convinced a problem has been stated incorrectly,
indicate your interpretation in writing your answer. In such cases, do not interpret the problem in
such a way that it becomes trivial.
Notes:
Each ring
R
referred to in this exam will be assumed to contain a multiplicative identify 1
R
. Every
left
R
module
M
will have the property that 1
R
·
m
=
m
for all
m
∈
M
, and every homomorphism of
rings
ϕ
:
R
→
S
will be assumed to satisfy the property that
ϕ
(1
R
) = 1
S
.
is the field of rational
numbers,
the field of real numbers,
the field of complex numbers,
the ring of integers, and
q
a finite field with
q
elements.
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 Spring '08
 comech
 Vector Space, 12pts, 14pts, field.

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