Factorization in rings of integer-valued rational functions

Abstract

For a domain D, the ring $\text{Int}(D)$ of integer-valued polynomials over D is atomic if D satisfies the ascending chain condition on principal ideals. However, even for a discrete valuation domain V, the ring ${\text{Int}}^{\mathrm{R}}(V)$ of integer-valued rational functions over V is antimatter. We introduce a family of atomic rings of integer-valued rational functions and study various factorization properties in these rings.

KEYWORDS:

• Antimatter
• ring of integer-valued rational functions
• ring of integer-valued polynomials

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13F15
• 13A05
• 13A18
• 13F20