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

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...

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

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

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

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

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

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)...

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...

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...

real closed field. It can be thought of as a real analogue of Hilbert's Nullstellensatz (which concern complex zeros of polynomial ideals), and this analogy...

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

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...

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...

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...

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

20th century to try to "eliminate elimination". Nevertheless Hilbert's Nullstellensatz, may be considered to belong to elimination theory, as it asserts...

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...

analysis used to study complex varieties do not seem to apply. Hilbert's Nullstellensatz suggests an approach to algebraic geometry over any algebraically...

field k {\displaystyle k} . This is a geometric formulation of Hilbert's Nullstellensatz. In the above example, the points of the first kind are closed...

{\displaystyle M} . The primary motivation in studying radicals is Hilbert's Nullstellensatz in commutative algebra. One version of this celebrated theorem...

embedding theorem (group theory) Hilbert's basis theorem (commutative algebra,invariant theory) Hilbert's Nullstellensatz (theorem of zeroes) (commutative...

theorem to polynomials with quaternionic coefficients and variables Hilbert's Nullstellensatz, a generalization to several variables of the assertion that complex...

logic Hilbert space – Type of topological vector space Hilbert's Nullstellensatz – Relation between algebraic varieties and polynomial ideals Hilbert's syzygy...

combination (with polynomial coefficients) of the equations (this is Hilbert's Nullstellensatz). If an underdetermined system of t equations in n variables (t...

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...