Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids
By Víctor Blanco, Pedro A. García-Sánchez, Alfred Geroldinger. 2010
69 citations recorded by the source corpus.
Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/126e93c860847c530d8aaf7b1759d815129b661b
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In Algebra and Number Theory
In Computational Theory and Mathematics
Citations in the corpus
- On strongly primary monoids, with a focus on Puiseux monoids (2019, background): “In special cases (such as for numerical monoids generated by arithmetic sequences or Puiseux monoids generated by geometric sequences) very explicit descriptions of sets of lengths and their unions are available (in these cases, the initial and end parts are empty; see [1, 9, 11]).”
- Factorization invariants of Puiseux monoids generated by geometric sequences (2019, background): “Unions of sets of lengths have received a great deal of attention in recent literature; see, for example, [4, 7, 15, 41].”
- On the delta set and the Betti elements of a BF-monoid (2012, unknown): “As we mentioned above, c(S) = max{c1, r12 + r13, c2, r21 + r23, c3, r31 + r32} (and also equal to t(S), the tame degree of S, and ω(S), the ω-primality of S; see [4] for details).”