2022/08/21 by Liu, Baian
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2208.09935
\DeclareMathOperator\IntRIntRInteger-valued rational functions are a natural generalization of integer-valued polynomials. Given a domain D, the collection of all integer-valued rational functions over D forms a ring extension \IntR(D) of D. For a valuation domain V, we characterize when \IntR(V) is a Prüfer domain and when \IntR(V) is a Bézout domain. We also extend the classification of when \IntR(D) is a Prüfer domain.