- In mathematics, Hilbert's
Nullstellensatz (German for "theorem of zeros", or more literally, "zero-locus-theorem") is a
theorem that
establishes a fundamental...
- {x}})} . This
result is
known as the
Hilbert root theorem, or "Hilberts
Nullstellensatz" in German. He also
proved that the
correspondence between vanishing...
- 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)...
- the
Nullstellensatz fails as the real
numbers are not
algebraically closed. However, one can
recover a
similar theorem, the real
Nullstellensatz, by using...
- Hilbert's
Nullstellensatz provides a
fundamental correspondence between ideals of
polynomial rings and
algebraic sets.
Using the
Nullstellensatz and related...
- In mathematics, the Weierstr****
Nullstellensatz is a
version of the
intermediate value theorem over a real
closed field. It says:
Given a
polynomial f...
-
proving the
general case of the
Hilbert Nullstellensatz from an
easier special case (the so-called weak
Nullstellensatz), by
introducing an
extra variable...
-
which field a
particular result belongs to. For example, Hilbert's
Nullstellensatz is a
theorem which is
fundamental for
algebraic geometry, and is stated...
-
David Hilbert because of
their relation to Hilbert's
Nullstellensatz. Hilbert's
Nullstellensatz of
algebraic geometry is a
special case of the statement...
-
influential proof by
contradiction was
given by
David Hilbert. His
Nullstellensatz states: If f 1 , … , f k {\displaystyle f_{1},\ldots ,f_{k}} are polynomials...
