JournalspmVol. 66 / No. 1DOI 10.4171/pm/1830

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

  • David E. Dobbs

    University of Tennessee, Knoxville, United States
A class of integral domains whose integral closures are small submodules of the quotient field cover

You need to subscribe to download the article.

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.