A nilregular element property (Q2487024)

A theorem stating that if a ring \(R\) is noetherian, then every nilregular ideal contains a nilregular element is constructively proved. The proof provides an algorithm to produce nilregular elements of nilregular ideals whenever \(R\) is coherent, noetherian and discrete. As an application, a constructive proof is provided of the Eisenbud-Evans-Storch theorem that every algebraic set in \(n\)-dimensional affine space is the intersection of \(n\) hypersurfaces.