# A class of integral domains whose integral closures are small submodules of the quotient field

### David E. Dobbs

University of Tennessee, Knoxville, United States

## Abstract

Let $(V, M)$ be a valuation domain which is distinct from its quotient field $K$, and let $π:V→V/M$ be the canonical surjection. Let $D$ be a subring of $V/M$. It is proved that the pullback $R:=π_{−1}(D)$ has the property that $V$ (and hence each integral overring of $R$) is a small $R$-submodule of $K$. Applications include all classical $D+M$ constructions and locally pseudo-valuation domains.

## Cite this article

David E. Dobbs, A class of integral domains whose integral closures are small submodules of the quotient field. Port. Math. 66 (2009), no. 1, pp. 65–70

DOI 10.4171/PM/1830