Kronecker Function Rings and Prüfer-Like Domains

Abstract

Let D be an integral domain,D be the integral closure of D, * be a star operation of finite character on D, * w be the so-called * w-operation on D induced by * , X be an indeterminate over D, N * = {f ∈ D[X]|c(f) * = D}, and Kr(D, *) = {0} ∪ { f g |0 = f, g ∈ D[X] and there is an 0 = h ∈ D[X] such that (c(f)c(h)) * ⊆ (c(g)c(h)) * }. In this paper, we show that D is a *-quasi-Prüfer domain if and only ifD[X] N * = Kr(D, * w). As a corollary, we recover Fontana-Jara-Santos's result that D is a Prüfer *-multiplication domain if and only if D[X] N * = Kr(D, * w).