Factorization in one-dimensional integral domains and their ideal monoids

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 [Formula: see text]-absorbing ideals in those rings. Examples and applications on nonprincipal orders of quadratic number fields are also presented.