 Work in the 1920s of B. L. van der Waerden had already addressed the question; in the Italian school of algebraic geometry the ideas were well known, but foundational questions were not addressed in the same spirit.A well-working machinery of intersecting algebraic cycles and requires more than taking just the set-theoretic intersection of the cycles in question.If the two cycles are in "good position" then the "intersection product", denoted , should consist of the set-theoretic intersection of the two subvarieties.