40 citations · 282 across the 43 of their papers we have counts for
6 papers · 2 filters
The system of sets of lengths in Krull monoids under set addition
Alfred Geroldinger, Wolfgang Schmid
Let be a Krull monoid with class group and suppose that each class contains a prime divisor. Then every element has a factorization into irreducible elements, and…
The catenary degree of Krull monoids II
Alfred Geroldinger, Qinghai Zhong
Let be a Krull monoid with finite class group such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy r…
A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems
Nicholas R. Baeth, Alfred Geroldinger, David J. Grynkiewicz +1
Let be a ring and let be a small class of right -modules which is closed under finite direct sums, direct summands, and isomorphisms. Let $\mathcal V (\mathcal…
The set of minimal distances in Krull monoids
Alfred Geroldinger, Qinghai Zhong
Let be a Krull monoid with finite class group . Then every non-unit can be written as a finite product of atoms, say . The set $\math…
Monoids of modules and arithmetic of direct-sum decompositions
Nicholas R. Baeth, Alfred Geroldinger
Let be a (possibly noncommutative) ring and let be a class of finitely generated (right) -modules which is closed under finite direct sums, direct summands, and…
On v-Marot Mori rings and C-rings
Alfred Geroldinger, Sebastian Ramacher, Andreas Reinhart
C-domains are defined via class semigroups, and every C-domain is a Mori domain with nonzero conductor whose complete integral closure is a Krull domain with finite class group. In…