# affine algebraic in a sentence

1) Thus it is an

**affine**

**algebraic**variety.

algebraic collocations

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 sentences

4) 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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