affine algebraic in a sentence
1) Thus it is an affine algebraic variety.
2) An irreducible affine algebraic set is also called an affine variety.
3) Affine varieties can be given a natural topology by declaring the closed sets to be precisely the affine algebraic sets.
affine algebraic example sentences4) The general linear group "GL""n" is an affine algebraic variety that can be viewed as the multiplicative group of the "n" by "n" matrix ring variety.
5) If "X" is an affine algebraic variety, then the set of all regular functions on "X" forms a ring called the coordinate ring of "X".
6) For any affine algebraic set "V", the coordinate ring or structure ring of "V" is the quotient of the polynomial ring by this ideal.
7) A nonempty affine algebraic set "V" is called irreducible if it cannot be written as the union of two proper algebraic subsets.
8) A subset "V" of __FORMULA__ is called an affine algebraic set if "V" = "Z"("S") for some "S".
9) The projective Zariski topology is defined for projective algebraic sets just as the affine one is defined for affine algebraic sets, by taking the subspace topology.
10) Like for affine algebraic sets, there is a bijection between the projective algebraic sets and the reduced homogeneous ideals which define them.
11) The Grassmannian as a real affine algebraic variety
12) (Many authors use the phrase "affine variety" to refer to any affine algebraic set, irreducible or not)
13) Every affine algebraic curve of equation "p"("x", "y") = 0 may be completed into the projective curve of equation __FORMULA__ where
14) Affine algebraic variety
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