  The elasticity of an atomic integral domain is, in some sense, a measure of
how far the domain is from being a unique factorization domain (or, more
properly, a half-factorial domain). We consider the relationship between the
elasticity of a domain, R, and the elasticity of its polynomial ring R[x]. For
example, if R has at least one atom, a sufficient condition for the polynomial
ring R[x] to have elasticity 1 is that every nonconstant irreducible polynomial
f in R[x] be irreducible in K[x]. We will determine the integral domains R
whose polynomial rings satisfy this condition.
