Derivations and integral closure

A. Seidenberg

Vol. 16 (1966), No. 1, 167–173

DOI: 10.2140/pjm.1966.16.167

Abstract

Let 𝒪 be an integral domain containing the rational numbers, Σ its quotient field, D a derivation of Σ, and 𝒪′ the ring of elements in Σ quasi-integral over 𝒪. It is shown that if D𝒪⊂𝒪, then D𝒪′⊂𝒪′.

Mathematical Subject Classification

Primary: 13.60

Secondary: 13.80

Milestones

Received: 13 February 1964

Revised: 25 June 1964

Published: 1 January 1966