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arXiv:2309.14024math.AG

Early proofs of Hilbert's Nullstellensatz

Jan Stevens

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Abstract

By Rabinowitsch' trick Hilbert's Nullstellensatz follows from the weak Nullstellensatz (Rabinowitsch 1929). The weak version can be shown with elimination theory. Hilbert's original proof is also based on successive elimination. Lasker obtained a new proof using primary decomposition. We describe these early proofs and place them in the development of commutative algebra up to the appearance of van der Waerden's Moderne Algebra. We also explain Hentzelt's Nullstellensatz.

arXiv comments
33 p
Journal reference
DOI
Subjects
math.AGAlgebraic Geometry math.ACCommutative Algebra math.HOHistory and Overview

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