Sets of Arithmetical Invariants in Transfer Krull Monoids
arXiv:1805.02911 · doi:10.1016/j.jpaa.2018.12.011
Abstract
Transfer Krull monoids are a recent concept including all commutative Krull domains and also, for example, wide classes of non-commutative Dedekind domains. We show that transfer Krull monoids are fully elastic (i.e., every rational number between and the elasticity of the monoid can be realized as the elasticity of an element). In commutative Krull monoids which have sufficiently many prime divisors in all classes of their class group, the set of catenary degrees and the set of tame degrees are intervals. Without the assumption on the distribution of prime divisors, arbitrary finite sets can be realized as sets of catenary degrees and as sets of tame degrees.
References in corpus (14)
- Factorization theory: From commutative to noncommutative settings
- Sets of lengths in maximal orders in central simple algebras
- Power monoids: A bridge between Factorization Theory and Arithmetic Combinatorics
- The Catenary Degree of Krull Monoids I
- Factorizations in bounded hereditary Noetherian prime rings
- Systems of sets of lengths: Transfer Krull monoids versus weakly Krull monoids
- The Realization Problem for Delta Sets of Numerical Semigroups
- On the set of elasticities in numerical monoids
- Factorizations of Elements in Noncommutative Rings: A Survey
- The catenary degree of Krull monoids II
- On the set of catenary degrees of finitely generated cancellative commutative monoids
- Factoriality and class groups of cluster algebras
- Sets of minimal distances and characterizations of class groups of Krull monoids
- Realizable sets of catenary degrees of numerical monoids
Cited by in corpus (7)
- On elasticities of locally finitely generated monoids
- On the system of sets of lengths and the elasticity of submonoids of a finite-rank free commutative monoid
- Lattices over Bass rings and graph agglomerations
- On noncommutative bounded factorization domains and prime rings
- Definite orders with locally free cancellation
- Factorization Theory in Commutative Monoids
- On product-one sequences over dihedral groups