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#hilbert's_syzygy_theorem

Hilbert's syzygy theorem

Theorem about linear relations in ideals and modules over polynomial rings

In mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in 1890, that were introduced for solving important open questions in invariant theory, and are at the basis of modern algebraic geometry. The two other theorems are Hilbert's basis theorem, which asserts that all ideals of polynomial rings over a field are finitely generated, and Hilbert's Nullstellensatz, which establishes a bijective correspondence between affine algebraic varieties and prime ideals of polynomial rings.

Tue 30th

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Hilbert's syzygy theorem Linear relation Hilbert's theorem Hilbert's basis theorem Noetherian ring David Hilbert Hilbert series and Hilbert polynomial Hilbert's twenty-fourth problem Polynomial ring List of theorems

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