We compute various algebraic invariants that measure the failure of unique factorization in atomic monoids and integral domains. In doing so, we focus on one-dimensional Noetherian domains, especially the orders of a Dedekind domain including numerical semigroup power series rings and Bass rings, along with the behavior of n-absorbing ideals in those rings. Examples and applications on nonprincipal orders of quadratic number fields are also presented.
Hyun Seung Choi (Thu,) studied this question.