PMA427
SCHOOL OF MATHEMATICS AND STATISTICS
Spring Semester 20072008
Galois Theory
Answer
four
2 hours 30 minutes
questions. If you answer more than four questions, only your best four will
be counted.
Notation: Z denotes the integers and Q the rationals.
PMA427 GALOIS THEORY EXAM SOLUTIONS 2006/07
(i) A K -automorphism of L is a function : L L such that:
is a ring homomorphism, so (0) = 0, (1) = 1, (a + b) = (a) + (b) and (ab) =
(a)(b) for all a, b L.
is a bijection.
For all a K we have (a) = a.
The Ga
SCHOOL OF MATHEMATICS AND STATISTICS
Galois Theory
Of
PMA427
University
Shefeld.
Spring Semester 20062007
2 hours 30 minutes
Answer four questions. If you answer more than four questions, only your best four will
be counted.
In this exam, as in