Minimal relations and catenary degrees in Krull monoids

On Minimal Distances in Krull Monoids with Infinite Class Group

Let H be a Krull monoid with infinite class group such that each divisor class contains a prime divisor. We show that for every positive integer n, there exists a divisor closed submonoid S of H such that min∆(S) = n.

Local and global tameness in Krull monoids

Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. Then the global tame degree t(H) equals zero if and only if H is factorial (equivalently, |G| = 1). If |G| > 1, then D(G) ≤ t(H) ≤ 1 + D(G) (

The catenary degrees of elements in numerical monoids of embedding dimension three

On the set of catenary degrees of finitely generated cancellative commutative monoids

The catenary degree of an element s of a cancellative commutative monoid S is a nonnegative integer measuring the distance between the irreducible factorizations of s. The catenary degree of the monoid S, defined as the supremum over all catenary degrees occurring in S, has been heavily studied as an invariant of nonunique factorization. In this paper, we investigate the set C(S) of catenary de...

A New Characterization of Half-factorial Krull Monoids

Let M be a Krull monoid. Then every element of M may be written as a finite product of irreducible elements. If for every a ∈ M , each two factorizations of a have the same number of irreducible elements, then M is called half-factorial. Using a property of element exponentiation, we provide a new characterization of half-factoriality, valid for all Krull monoids whose class group has torsion-f...