27 citations · 64 across the 13 of their papers we have counts for
10 papers · 1 filter
Minimal generating sets of large powers of bivariate monomial ideals
Jutta Rath, Roswitha Rissner
It is known that for a monomial ideal , the number of minimal generators, , eventually follows a polynomial pattern for increasing . In general, little is known about…
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…
Stabilization of associated prime ideals of monomial ideals -- Bounding the copersistence index
Clemens Heuberger, Jutta Rath, Roswitha Rissner
The sequence of associated primes of powers of a monomial ideal in a polynomial ring eventually stabilizes by a known result…
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…
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…
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 with finite residue field, it is known that there exist absolutely irreduc…
Absolute irreducibility of the binomial polynomials
Roswitha Rissner, Daniel Windisch
In this paper we investigate the factorization behaviour of the binomial polynomials and their powers in the ring of integer-valued…
Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields
Sophie Frisch, Sarah Nakato, Roswitha Rissner
Let be a Dedekind domain with infinitely many maximal ideals, all of finite index, and its quotient field. Let …
Computing -ideals of a matrix over a principal ideal domain
Clemens Heuberger, Roswitha Rissner
Given a square matrix over a principal ideal domain and an ideal of , the -ideal of consists of the polynomials such that all entries of ar…
Null ideals of matrices over residue class rings of principal ideal domains
Roswitha Rissner
Given a square matrix with entries in a commutative ring , the ideal of consisting of polynomials with is called the null ideal of . Very little is k…