Integer-Valued Polynomial Rings, 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) ∈ K[X]: f(D) ⊂ D} of the polynomial ring K[X]. Using the tools of t-closure and associated primes, we generalize some known results on integer-valued polynomial rings over Krull domains, Prüfer v-multiplication domains, and Mori domains.

Key Words:

• Associated prime
• Integer-valued polynomial
• Integral domain
• t-closure

2000 Mathematics Subject Classification:

• 13F20
• 13G05
• 13F05
• 13A15
• 13B25

Notes

Communicated by I. Swanson.