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.
Dr. Stefan Tohaneanu, Department of Mathematics, University of Idaho
Anzis, Benjamin E.
"Irreducibility and Factors of Polynomials in Noetherian Integral Domains,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 2.
Available at: http://scholar.rose-hulman.edu/rhumj/vol15/iss2/2