40 citations · 282 across the 43 of their papers we have counts for
42 papers · 1 filter
There is no polynomial formula for the catenary and the tame degree of finitely generated monoids
Alfred Geroldinger, Alessio Moscariello
In the last two decades there has been a wealth of results determining the precise value of the catenary degree and the tame degree. Mostly, however, only for very special classes…
On Long-Term Problems in Multiplicative Ideal Theory and Factorization Theory
Alfred Geroldinger, Hwankoo Kim, K. Alan Loper
In this survey article we discuss key open problems which could serve as a guidance for further research directions of multiplicative ideal theory and factorization theory.
On conductor submonoids of factorial monoids
Alfred Geroldinger, Weihao Yan, Qinghai Zhong
We study algebraic and arithmetic properties of submonoids (resp. subrings) of factorial monoids (resp. factorial domains) whose non-invertible elements all lie in the conductor. T…
On Sets of Lengths in Monoids of plus-minus weighted Zero-Sum Sequences
Alfred Geroldinger, Florian Kainrath
Let be an additive abelian group. A sequence of terms from is a plus-minus weighted zero-sum sequence if there are $\varepsilon_1, \ld…
On monoid algebras having every nonempty subset of as a length set
Alfred Geroldinger, Felix Gotti
We construct monoid algebras which satisfy the ascending chain condition on principal ideals and which have the property that every nonempty subset of occurs a…
On Dedekind domains whose class groups are direct sums of cyclic groups
Gyu Whan Chang, Alfred Geroldinger
For a given family of finitely generated abelian groups, we construct a Dedekind domain having the following properties. \begin{enumerate} \item $\Pic(D) \co…