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Affine variety
In
algebraic geometry
, an
affine variety
over an
algebraically closed field
k
is the zero-locus in the
affine n-space
of some finite family of
polynomials
of
n
variables with coefficients in
k
that generate a
prime ideal
. If the condition of generating a prime ideal is removed, such a set is called an (affine)
algebraic set
. A
Zariski open
subvariety of an affine variety is called a
quasi-affine variety
.
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