Elasticity of factorizations in R 0 + X R1 + … + X lRl [X

Abstract

For an atomic domain R the elasticity ρ(R) is defined by ρ(R) = sup{m/n ¦ u1 … um = v1 … vn where ui, vi∈ R are irreducible}. Let R0 ⊂ … ⊂ Rl be an ascending chain of domains which are finitely generated over ℤ and assume that Rl is integral over R0. Let X be an indeterminate. In this paper we characterize all domains D of the form D = R0 + XR1 + … + XlRl[X] whose elasticity ρ(D) is finite.