Roswitha Rissner

activity

20142025

most citedSets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields

27 citations · 64 across the 13 of their papers we have counts for

collaborators

13 papers

math.AC2025

Minimal generating sets of large powers of bivariate monomial ideals

Jutta Rath, Roswitha Rissner

It is known that for a monomial ideal $I$ , the number of minimal generators, $μ (I^{n})$ , eventually follows a polynomial pattern for increasing $n$ . In general, little is known about…

math.AC2024

Irreducible integer-valued polynomials with prescribed minimal power that factors non-uniquely

Sarah Nakato, Roswitha Rissner

We study the question up to which power an irreducible integer-valued polynomial that is not absolutely irreducible can factor uniquely. For example, for integer-valued polynomials…

math.RA2024

Counting core sets in matrix rings over finite fields

Roswitha Rissner, Nicholas J. Werner

Let $R$ be a commutative ring and $M_{n} (R)$ be the ring of $n \times n$ matrices with entries from $R$ . For each $S \subseteq M_{n} (R)$ , we consider its (generalized) null ideal $N(S)…

math.AC2023

Stabilization of associated prime ideals of monomial ideals -- Bounding the copersistence index

Clemens Heuberger, Jutta Rath, Roswitha Rissner

The sequence $(Ass (R / I^{n}))_{n \in N}$ of associated primes of powers of a monomial ideal $I$ in a polynomial ring $R$ eventually stabilizes by a known result…

math.AC2023

Fluctuations in depth and associated primes of powers of ideals

Roswitha Rissner, Irena Swanson

We count the numbers of associated primes of powers of ideals as defined by Bandari, Hibi, and Herzog in 2014. We generalize those ideals to monomial ideals $\operatorname{BHH}(m,r…

math.AC2022★ 1 cited

Characterizing absolutely irreducible integer-valued polynomials over discrete valuation domains

Moritz Hiebler, Sarah Nakato, Roswitha Rissner

Rings of integer-valued polynomials are known to be atomic, non-factorial rings furnishing examples for both irreducible elements for which all powers factor uniquely (\emph{absolu…

math.AC2021

Split absolutely irreducible integer-valued polynomials over discrete valuation domains

Sophie Frisch, Sarah Nakato, Roswitha Rissner

Regarding non-unique factorization of integer-valued polynomials over a discrete valuation domain $(R, M)$ with finite residue field, it is known that there exist absolutely irreduc…

math.AC2020★ 9 cited

Absolute irreducibility of the binomial polynomials

Roswitha Rissner, Daniel Windisch

In this paper we investigate the factorization behaviour of the binomial polynomials $(n x) = \frac{x ( x - 1 ) \dots ( x - n + 1 )}{n !}$ and their powers in the ring of integer-valued…

math.CO2020

Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory

Ayman Badawi, Roswitha Rissner

For a partially ordered set $(A, \leq)$ , let $G_{A}$ be the simple, undirected graph with vertex set $A$ such that two vertices $a \neq = b \in A$ are adjacent if either $a \leq b$ or $b…

math.AC2017★ 27 cited

Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields

Sophie Frisch, Sarah Nakato, Roswitha Rissner

Let $D$ be a Dedekind domain with infinitely many maximal ideals, all of finite index, and $K$ its quotient field. Let $Int (D) = {f \in K [x] ∣ f (D) \subseteq D}$ …

math.AC2016★ 5 cited

Computing $J$ -ideals of a matrix over a principal ideal domain

Clemens Heuberger, Roswitha Rissner

Given a square matrix $B$ over a principal ideal domain $D$ and an ideal $J$ of $D$ , the $J$ -ideal of $B$ consists of the polynomials $f \in D [X]$ such that all entries of $f (B)$ ar…

math.AC2015★ 9 cited

Null ideals of matrices over residue class rings of principal ideal domains