6 citations · 6 across the 2 of their papers we have counts for
8 papers
On transfer Krull monoids
Aqsa Bashir, Andreas Reinhart
Let be a cancellative commutative monoid, let be the set of atoms of and let be the root closure of . Then is called transfer Krull…
On finite molecularization domains
Andrew J. Hetzel, Anna L. Lawson, Andreas Reinhart
In this paper, we advance an ideal-theoretic analogue of a "finite factorization domain" (FFD), giving such a domain the moniker "finite molecularization domain" (FMD). We characte…
Unique factorization property of non-unique factorization domains II
Gyu Whan Chang, Andreas Reinhart
Let be an integral domain. A nonzero nonunit of is called a valuation element if there is a valuation overring of such that . We say that is a…
Radical factorization in finitary ideal systems
Bruce Olberding, Andreas Reinhart
In this paper we investigate the concept of radical factorization with respect to finitary ideal systems of cancellative monoids. We present new characterizations for r-almost Dede…
On monoids of ideals of orders in quadratic number fields
Johannes Brantner, Alfred Geroldinger, Andreas Reinhart
We determine the set of catenary degrees, the set of distances, and the unions of sets of lengths of the monoid of nonzero ideals and of the monoid of invertible ideals of orders i…
Radical factorization in commutative rings, monoids and multiplicative lattices
Bruce Olberding, Andreas Reinhart
In this paper we study the concept of radical factorization in the context of abstract ideal theory in order to obtain a unified approach to the theory of factorization into radica…