The Catenary and Tame Degree in Finitely Generated Commutative Cancellative Monoids

By Scott T. Chapman, P. García-Sánchez, David Llena, V. Ponomarenko, José Carlos Rosales. 2006

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Power monoids: A bridge between factorization theory and arithmetic combinatorics (2017, result): “Further contributions to this line of research have been made, among others, by Chapman, Gotti, and Pelayo [12], García-García, Moreno-Frías, and Vigneron-Tenorio [23], and Chapman, García-Sánchez, Llena, Ponomarenko, and Rosales [10].”
On the arithmetic of tame monoids with applications to Krull monoids and Mori domains (2010, background): “Tameness implies a variety of further arithmetical finiteness properties (such as the finiteness of the catenary degree and of the elasticity), and local tameness is a central finiteness property in factorization theory (we refer to the monograph [22] and some recent publications [9,8,27]).”
Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids (2010, background): “The next lemma is a generalization of Lemma 5 in [8].”
Local tameness of v-noetherian monoids (2008, background): “Recent results on this invariant can be found in [1,3,4,17,18].”