Andreas Reinhart

activity

20142023

most citedUnique factorization property of non-unique factorization domains II

6 citations · 6 across the 5 of their papers we have counts for

collaborators

16 papers

math.NT2023

On orders in quadratic number fields with unusual sets of distances

Andreas Reinhart

Let $O$ be an order in an algebraic number field and suppose that the set of distances $Δ (O)$ of $O$ is nonempty (equivalently, $O$ is not h…

math.AC2023

On Monoids of plus-minus weighted Zero-Sum Sequences: The Isomorphism Problem and the Characterization Problem

Florin Fabsits, Alfred Geroldinger, Andreas Reinhart +1

Let $G$ be an additive abelian group. A sequence $S = g_{1} \cdot \dots \cdot g_{ℓ}$ of terms from $G$ is a plus-minus weighted zero-sum sequence if there are $\varepsilon_1,\ldots,\v…

math.AC2021

On transfer Krull monoids

Aqsa Bashir, Andreas Reinhart

Let $H$ be a cancellative commutative monoid, let $A (H)$ be the set of atoms of $H$ and let $H$ be the root closure of $H$ . Then $H$ is called transfer Krull…

math.AC2021

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…

math.AC2020

Commutative rings with one-absorbing factorization

Abdelhaq El Khalfi, Mohammed Issoual, Najib Mahdou +1

Let $R$ be a commutative ring with nonzero identity. A. Yassine et al. defined in the paper (Yassine, Nikmehr and Nikandish, 2020), the concept of $1$ -absorbing prime ideals as fol…

math.AC2020

On the arithmetic of stable domains

Aqsa Bashir, Alfred Geroldinger, Andreas Reinhart

A commutative ring $R$ is stable if every non-zero ideal $I$ of $R$ is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have recei…

math.AC2020★ 6 cited

Unique factorization property of non-unique factorization domains II

Gyu Whan Chang, Andreas Reinhart

Let $D$ be an integral domain. A nonzero nonunit $a$ of $D$ is called a valuation element if there is a valuation overring $V$ of $D$ such that $aV \cap D = a D$ . We say that $D$ is a…

math.AC2019

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…

math.AC2019

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…

math.AC2018

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…

math.AC2017

The monotone catenary degree of monoids of ideals

Alfred Geroldinger, Andreas Reinhart

Factoring ideals in integral domains is a central topic in multiplicative ideal theory. In the present paper we study monoids of ideals and consider factorizations of ideals into m…

math.AC2016

On the divisor-class group of monadic submonoids of rings of integer-valued polynomials

Andreas Reinhart

Let $R$ be a factorial domain. In this work we investigate the connections between the arithmetic of $Int (R)$ (i.e., the ring of integer-valued polynomials over $R$ ) and its…

math.AC2015

Group-theoretic and topological invariants of completely integrally closed Prüfer domains

Olivier A. Heubo-Kwegna, Bruce Olberding, Andreas Reinhart

We consider the lattice-ordered groups Inv $(R)$ and Div $(R)$ of invertible and divisorial fractional ideals of a completely integrally closed Prüfer domain. We prove that Div $(R)$ …

math.AC2015

A note on conductor ideals

Andreas Reinhart

Let $S$ be a commutative ring with identity and $R$ a unitary subring of $S$ . An ideal $I$ of $S$ is called an $R$ -conductor ideal of $S$ if $I = {x \in S ∣ x S \subseteq V}$ for so…

math.AC2015

Arithmetic of seminormal weakly Krull monoids and domains

Alfred Geroldinger, Florian Kainrath, Andreas Reinhart

We study the arithmetic of seminormal $v$ -noetherian weakly Krull monoids with nontrivial conductor which have finite class group and prime divisors in all classes. These monoids i…

math.AC2014

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…