Abstract
In a paper which will follow shortly in these Annals, we shall treat the analytical theory of the singular solutions of partial differential equations of the first order. It appears desirable to make clear first the nature of the irreducible components of the manifold of a partial differential polynomial (p.d.p. or even d.p.). We first define and discuss the general solution of an algebraically irreducible p.d.p. It is then proved that every irreducible component of the manifold of a p.d.p. is the general solution of some p.d.p.; that is, the prime ideal corresponding to the component has a basic set composed of a single d.p. This result generalizes a theorem previously established for ordinary differential polynomials.2
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