On the arithmetic of tame monoids with applications to Krull monoids and Mori domains

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Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids (2010, background): “2) measure in particular how far away atoms are from primes (see [29], [28], [27], [30]).”
Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules (2016, background): “In the next proposition we collect some elementary properties of the above invariants that are well-known for cancellative monoids ([24, 25]).”