Systems of sets of lengths: Transfer Krull monoids versus weakly Krull monoids

Abstract

Transfer Krull monoids are monoids which allow a weak transfer homomorphism to a commutative Krull monoid, and hence the system of sets of lengths of a transfer Krull monoid coincides with that of the associated commutative Krull monoid. We unveil a couple of new features of the system of sets of lengths of transfer Krull monoids over finite abelian groups G, and we provide a complete description of the system for all groups G having Davenport constant D(G) = 5 (these are the smallest groups for which no such descriptions were known so far). Under reasonable algebraic finiteness assumptions, sets of lengths of transfer Krull monoids and of weakly Krull monoids satisfy the Structure Theorem for Sets of Lengths. In spite of this common feature we demonstrate that systems of sets of lengths for a variety of classes of weakly Krull monoids are different from the system of sets of lengths of any transfer Krull monoid.

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Cited by in corpus (10)

• Structural properties of subadditive families with applications to factorization theory
• Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields
• Sets of Arithmetical Invariants in Transfer Krull Monoids
• Long sets of lengths with maximal elasticity
• On elasticities of locally finitely generated monoids
• A characterization of length-factorial Krull monoids
• A characterization of finite abelian groups via sets of lengths in transfer Krull monoids
• Factorization Theory in Commutative Monoids
• On product-one sequences over dihedral groups
• On transfer Krull monoids