32 citations · 113 across the 18 of their papers we have counts for
9 papers · 1 filter
On the incomparability of systems of sets of lengths
Alfred Geroldinger, Wolfgang Schmid
Let be a Krull monoid with finite class group such that every class contains a prime divisor. We consider the system of all sets of lengths of and stud…
A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions
Alfred Geroldinger, Wolfgang Schmid
Let H be a Krull monoid with finite class group G and suppose that every class contains a prime divisor. Then sets of lengths in H have a well-defined structure which just depends…
Which sets are sets of lengths in all numerical monoids ?
Alfred Geroldinger, Wolfgang Schmid
We explicitly determine those sets of nonnegative integers which occur as sets of lengths in all numerical monoids.
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…
Some recent results and open problems on sets of lengths of Krull monoids with finite class group
Wolfgang Schmid
Some of the fundamental notions related to sets of lengths of Krull monoids with finite class group are discussed, and a survey of recent results is given. These include the elasti…