Elasticity Properties Preserved in the Normset

Let T⊆R be the rings of integers in a number field and a finite Galois extension field. We study relations between the elasticity ρ(R) of the monoid of nonzero elements of R and the elasticity ρ(S) of the monoid S of norms to T of those elements. We show ρ(R)?ρ(S) and that equality holds if the norms of irreducible elements of R are irreducible in S, which is true, in particular, if either ρ(R)<2 or ρ(S)=1.