最終更新日：2025/12/05
(mathematics) A result about injectivity and surjectivity of polynomials, often given as this special case: If P is an injective polynomial function from an n-dimensional complex vector space to itself then P is bijective. The full theorem generalizes to any algebraic variety over an algebraically closed field.
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Ax-Grothendieck theorem
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元となった辞書の項目
Ax-Grothendieck theorem
固有名詞
(mathematics)
A
result
about
injectivity
and
surjectivity
of
polynomials,
often
given
as
this
special
case:
If
P
is
an
injective
polynomial
function
from
an
n-dimensional
complex
vector
space
to
itself
then
P
is
bijective.
The
full
theorem
generalizes
to
any
algebraic
variety
over
an
algebraically
closed
field.
日本語の意味
（数学）多項式の単射性と全射性に関する定理。具体的には、n次元複素ベクトル空間上の多項式写像が単射であれば、その写像は全単射であるという特別な場合が示され、この定理は任意の代数閉体上の任意の代数多様体に対して一般化される。
意味（1）
(mathematics)
A
result
about
injectivity
and
surjectivity
of
polynomials,
often
given
as
this
special
case:
If
P
is
an
injective
polynomial
function
from
an
n-dimensional
complex
vector
space
to
itself
then
P
is
bijective.
The
full
theorem
generalizes
to
any
algebraic
variety
over
an
algebraically
closed
field.
（ canonical ）
