Andreas Reinhart

collaborators

6 papers

math.AC2025

On the system of length sets of power monoids

Andreas Reinhart

The set $P_{fin, 0} (N_{0})$ of all finite subsets of $N_{0}$ containing the zero element is a monoid with set addition as operation. If a set $A\in\mat…

math.NT2024

A counterexample to the Conjecture of Ankeny, Artin and Chowla

Andreas Reinhart

Let $p$ be a prime number with $p \equiv 1 mod 4$ , let $ω = \frac{1 + p}{2}$ , let $ε > 1$ be the fundamental unit of $Z [ω]$ and let $x$ and $y$ be the unique non…

math.AC2024

Valuation Ideal Factorization Domains

Gyu Whan Chang, Andreas Reinhart

An integral domain $D$ is a {\em valuation ideal factorization domain} (VIFD) if each nonzero principal ideal of $D$ can be written as a finite product of valuation ideals. Clearly…

math.AC2024

Multiplicative lattices with absorbing factorization

Andreas Reinhart, Gulsen Ulucak

In [24], Yassine et al. introduced the notion of 1-absorbing prime ideals in commutative rings with nonzero identity. In this article, we examine the concept of 1-absorbing prime e…

math.NT2024

On counterexamples to Mordell's Pellian Equation Conjecture and the AAC-Conjecture: a non-computer based approach

Andreas Reinhart

In this note, we discuss recently discovered counterexamples to Mordell's Pellian Equation Conjecture and the Ankeny-Artin-Chowla-Conjecture. We provide a verification of the count…

math.NT2024

A counterexample to the Pellian equation conjecture of Mordell

Andreas Reinhart

Let $d \geq 2$ be a squarefree integer, let $ω \in {d, \frac{1 + d}{2}}$ be such that $Z [ω]$ is the ring of algebraic integers of the real quadratic number field…