In mathematics, Hilbert's Nullstellensatz (German for "theorem of zeros", or more literally, "zero-locus-theorem") is a theorem that establishes a fundamental...

indeterminates for a recurrence on the indeterminates. Bézout's theorem, Hilbert's Nullstellensatz and Jacobian conjecture are among the most famous properties that...

hexagon. An influential proof by contradiction was given by David Hilbert. His Nullstellensatz states: If f 1 , … , f k {\displaystyle f_{1},\ldots ,f_{k}}...

are Hilbert's basis theorem, which asserts that all ideals of polynomial rings over a field are finitely generated, and Hilbert's Nullstellensatz, which...

irreducibility theorem Hilbert's Nullstellensatz Hilbert's theorem (differential geometry) Hilbert's Theorem 90 Hilbert's syzygy theorem Hilbert–Speiser theorem...

to the set of prime ideals of a commutative ring follows from Hilbert's Nullstellensatz, that establishes a bijective correspondence between the points...

inconsistent) if and only if 1 belongs to the ideal (this is Hilbert's Nullstellensatz), or, equivalently, if its Gröbner basis (for any monomial ordering)...

who named them Hilbert rings after David Hilbert because of their relation to Hilbert's Nullstellensatz. Hilbert's Nullstellensatz of algebraic geometry...

algebra. The prominent results in this direction are Hilbert's basis theorem and Hilbert's Nullstellensatz, which are the basis of the connection between algebraic...

mathematics Hilbert's basis theorem asserts that every ideal of a polynomial ring over a field has a finite generating set (a finite basis in Hilbert's terminology)...

decide which field a particular result belongs to. For example, Hilbert's Nullstellensatz is a theorem which is fundamental for algebraic geometry, and...

variety in the above sense). In some contexts (see, for example, Hilbert's Nullstellensatz), it is useful to distinguish the field k in which the coefficients...

result, Hilbert's Nullstellensatz provides a fundamental correspondence between ideals of polynomial rings and algebraic sets. Using the Nullstellensatz and...

Hilbert's seventeenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It concerns the expression...

autonomous subfield of geometry c. 1900, with a theorem called Hilbert's Nullstellensatz that establishes a strong correspondence between algebraic sets...

for solving previously considered problems seems to be Hilbert's Nullstellensatz and Hilbert's basis theorem. From a philosophical point of view, the...

is a singularity. Hence, over an algebraically closed field, Hilbert's Nullstellensatz guarantees that the quadratic form always has isotropic lines...

are zero on an affine algebraic set (this is a consequence of Hilbert's Nullstellensatz). If A is a square matrix, then the product of A with itself n...

Hilbert's theorem may refer to: Hilbert's theorem (differential geometry), stating there exists no complete regular surface of constant negative gaussian...

Both notions are important in algebraic geometry, because of Hilbert's Nullstellensatz. An element of a ring that is equal to its own square is called...

theory. Hilbert's tenth problem Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed...

this result to any number of polynomials and indeterminates is Hilbert's Nullstellensatz. As noted in the introduction, Bézout's identity works not only...

matrices have a common eigenvector can be interpreted as a result of Hilbert's Nullstellensatz: commuting matrices form a commutative algebra K [ A 1 , … , A...

factors in S[t]. Let k be an algebraically closed field. The Hilbert's Nullstellensatz (theorem of zeros) states that there is a natural one-to-one correspondence...

normalization lemma can be used as an important step in proving Hilbert's Nullstellensatz, one of the most fundamental results of classical algebraic geometry...

schemes) and algebraic ones (ideals); the touchstone result here is Hilbert's Nullstellensatz, which roughly speaking shows that there is a natural one-to-one...

other algebraic varieties. One of the main such properties is Hilbert's Nullstellensatz, which asserts that a hypersurface contains a given algebraic...

then A ⊗k B is an integral domain. This is a consequence of Hilbert's nullstellensatz, and, in algebraic geometry, it implies the statement that the...

… , x n ] {\displaystyle \mathbb {C} [x_{1},\ldots ,x_{n}]} , Hilbert's Nullstellensatz states that every maximal ideal is of the form ( x 1 − α 1 , …...

geometry) Hasse's theorem on elliptic curves (number theory) Hilbert's Nullstellensatz (theorem of zeroes) (commutative algebra, algebraic geometry)...