Over an algebraically closed field, establishes a precise correspondence between ideals of a polynomial ring and the algebraic sets they define as common zero loci. Proved by David Hilbert, it is the theorem that founds the dictionary between algebra and geometry at the heart of algebraic geometry.
Facts
StatementThe Nullstellensatz establishes a fundamental correspondence between the ideals of a polynomial ring over an algebraically closed field and the algebraic sets (varieties) they define, and is a foundational result of algebraic geometry. 1 Classification
Statement FormCharacterization Theorem 1 Connections
In Branch
Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Proved By
Sources
1. Hilbert's Nullstellensatz (Wikipedia)
Wikimedia FoundationLead section, opening sentence
Hilbert's Nullstellensatz (German for "theorem of zeros" or, more literally, "zero-locus-theorem") is a theorem that establishes a fundamental relationship between geometry and algebra.
Lead section, history clause on the 1893 paper
It was proven by David Hilbert in his second major paper on invariant theory in 1893
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