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.

Author Bio

Ben Anzis is a math and computer science double major at the University of Idaho. His primary areas of interest are commutative algebra, algebraic geometry, and algebraic number theory. He completed this paper under the guidance of Dr. Stefan Tohaneanu during his freshman year.Faculty Sponsor: Dr. Stefan Tohaneanu, Department of Mathematics, University of Idaho