27 citations · 36 across the 8 of their papers we have counts for
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Sets of Lengths of Integer-Valued Polynomials on Prime Ideals of Principal Ideal Domains
Zaituni Kansiime, Sholastica Luambano, Sarah Nakato +2
Let be a principal ideal domain with infinite spectrum such that for every nonzero prime ideal of , the residue field is finite. Let be the quotient field of $…
Primes and absolutely or non-absolutely irreducible elements in atomic domains
Victor Fadinger, Sophie Frisch, Sarah Nakato +2
We give examples of atomic integral domains satisfying each of the eight logically possible combinations of existence or non-existence of the following kinds of elements: 1) primes…
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…
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…
A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
Sophie Frisch, Sarah Nakato
An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into irreducibles. In the case of t…
Non-absolutely irreducible elements in the ring of Integer-valued polynomials
Sarah Nakato
Let be a commutative ring with identity. An element is said to be absolutely irreducible in if for all natural numbers , has essentially only one facto…
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 …