Let R be a Noetherian integral domain, and let f be a polynomial with coefficients in R. A question of great importance is whether f is irreducible. In this paper, we give a sufficient condition for f to be irreducible by looking at the content ideal of f. This result is then extended to show a connection between the height of a polynomial's (proper) content ideal and the maximal number of irreducible factors it can possess.
Anzis, Benjamin E.
"Irreducibility and Factors of Polynomials in Noetherian Integral Domains,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15:
2, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss2/2