4 papers
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…
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…