How many irreducibles are prime?

Abstract

In the first course in ring theory, we learn about primes and irreducible elements. An easy proof tells us that if an element is prime then it is irreducible. It is, therefore, very natural to ask the question “How many irreducibles are prime?” During the course of this thesis, we’ll be working with Number rings and would devise a way to quantify primes and irreducibles and seek an answer to this problem.