Chennai Mathematical Institute

Seminars




Annual Seminar for Mathematics Research Scholars
Date: Thursday, 05 October 2023
Time: 12:00 PM
Venue: Lecture Hall 801
On Euclidean rings

Suhita Hazra
Chennai Mathematical Institute.
05-10-23


Abstract

One of the standard examples of a PID which is not a Euclidean domain is the ring $$\Z\left[ \frac{1 +\sqrt{-19}}{2}\right]$$ which is the ring of integers of the number field \Q(\sqrt{-19})$. This begs the question whether we can have more such examples coming from number fields. This question is linked to one of the deepest and central conjectures in Number theory. The starting point of such investigations necessitates a general characterisation of Euclidean domains and in this talk we shall try to give a few glimpses of this theme.