Supervisor:
Gábor Megyesi
1
Project Title
Algebraic Number Theory
2
Category
Pure
3
Level
3/4
4
2
5
Semesters
(length of project)
Description
6
References
7
Prerequisite courses
The study of Diophantine equations such as Fermat’s equation
xn+yn=zn, leads to considering extensions of the rational or the
integers. For example, when trying to solve an equation of the
form x2- dy2=a in the integers, it is natural to factorise the
left-hand side as (x+y√d)(x-y√d). However, the ring of such
numbers may not have unique factorisation, but it was
discovered that ideals in such rings can always be factorised
into prime ideals. The project would involve developing the
theory of integers in algebraic number fields, the proof of
unique factorisation into prime ideals and applications to
Diophantine equations.
I Stewart, D Tall: Algebraic Number Theory, Chapman & Tall,
1987
MATH2012
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Additional notes