UNIQUE FACTORIZATION OF MONIC POLYNOMIALS

Abstract

Translate Article

Let R be a commutative integral domain with 1. It is trivial to see that in the polynomial ring R[X], any nonconstant monic polynomial can be factored into a product of nonconstant monic polynomials which are irreducible in R[X]. However, in an arbitrary domain, such a factorization need not be unique. We show uniqueness occurs exactly when R is integrally closed.