On conductor submonoids of factorial monoids

Abstract We study algebraic and arithmetic properties of submonoids (resp. subrings) of factorial monoids (resp. factorial domains) whose non-invertible elements all lie in the conductor. This continues earlier work of Baeth, Cisto, et al. On our way we answer several conjectures, formulated in their papers in the affirmative ( [1, Conjecture 4.16] and [6, Conjectures 7 and 13, and Section 9]).