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

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.

18 pages