40 citations · 282 across the 43 of their papers we have counts for
5 papers · 2 filters
Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules
Yushuang Fan, Alfred Geroldinger, Florian Kainrath +1
Let be a commutative semigroup with unit element such that every non-unit can be written as a finite product of irreducible elements (atoms). For every , let $…
A realization theorem for sets of distances
Alfred Geroldinger, Wolfgang Schmid
Let be an atomic monoid. The set of distances of is the set of all with the following property: there are irreducible elements $u\_1, \ldots, u\_k…
Systems of sets of lengths: Transfer Krull monoids versus weakly Krull monoids
Alfred Geroldinger, Wolfgang Schmid, Qinghai Zhong
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 coinci…
The set of distances in seminormal weakly Krull monoids
Alfred Geroldinger, Qinghai Zhong
The set of distances of a monoid or of a domain is the set of all with the following property: there are irreducible elements $u_1, \ldots, u_k, v_1, \ldots, v_{k…
Minimal relations and catenary degrees in Krull monoids
Yushuang Fan, Alfred Geroldinger
Let be a Krull monoid with class group . Then is factorial if and only if is trivial. Sets of lengths and sets of catenary degrees are well studied invariants descri…