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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.
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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. 65–70DOI 10.4171/PM/1830