Integer-valued polynomials, $t$-closure, and associated primes

TL;DR

This paper explores the structure of integer-valued polynomial rings over various integral domains using $t$-closure and associated primes, generalizing existing results across different domain classes.

Contribution

It introduces a general framework connecting $t$-closure and associated primes to integer-valued polynomials, extending known results beyond Krull, PVMD, and Mori domains.

Findings

Generalized results on integer-valued polynomial rings

Connected $t$-closure with polynomial properties

Extended understanding of associated primes in this context

Abstract

Given an integral domain $D$ with quotient field $K$, the ring of integer-valued polynomials on D is the subring $\{f (X) \in K[X]: f(D) \subset D\}$ of the polynomial ring $K[X]$. Using the related tools of $t$-closure and associated primes, we generalize some known results on integer-valued polynomial rings over Krull domains, PVMD's, and Mori domains.