ABSTRACT
Let R be a commutative ring with 1, and suppose that R is a unique factorization domain. Let k be the field of fractions of R, and consider R as imbedded in k.
f(x) = xN + aN−1xN−1 + aN−2xN−2 + . . .+ a2x2 + a1x+ a0
be a polynomial in R[x]. If p is a prime in R such that p divides every coefficient ai but p2
does not divide a0, then f(x) is irreducible in R[x], and is irreducible in k[x].
