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. 051023 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.
