4 papers · 1 filter
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.
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 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 the isomorphism problem for monoids of product-one sequences
Alfred Geroldinger, Jun Seok Oh
Let and be torsion groups. We prove that the monoids of product-one sequences over and over are isomorphic if and only if the groups and are iso…