3 papers
math.AC2026
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 $…
math.AC2025
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…
math.AC2025
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…