Intersections of algebraic and algebroid varieties

ideal, Bull.Amer.Math.Soc.vol.50 (1944) p. 93.If to is the intersection of all primary ideals of o which are contained in p, Op contains o/h) as a subring and is the ring of quotients (in the ordinary sense) of p/ro with respect to o/tt).The homomorphism which assigns to every element of o its residue class modulo ro is called the natural homomorphism of o into Op.Throughout this paper we reserve the name of "varieties" to the irreducible varieties over an algebraically closed field.The cross references in the present paper are made according to the following principle: if no indication of section is given, the reference refers to some statement or formula contained in the same section; a similar convention holds if no indication of part is given.The propositions, lemmas, formulas and definitions are numbered starting with 1 in each section; the theorems are numbered starting with 1 in each part.