# Euclidean rings

**Project level:** PhD

Euclidean rings are algebraic structures generalizing the set of integers. Like the integers they have a division algorithm and unique factorization. Historically it has proved very difficult to determine if a ring is Euclidean or not but there have been several recent breakthroughs which are ripe for exploitation. This project could shed light on a famous conjecture of Gauss concerning unique factorization.