# affine algebraic set造句

## 例句与造句

1. Affine varieties can be given a natural topology by declaring the closed sets to be precisely the affine algebraic sets.
2. Like for affine algebraic sets, there is a bijection between the projective algebraic sets and the reduced homogeneous ideals which define them.
3. 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.
4. A nonempty affine algebraic set " V " is called "'irreducible "'if it cannot be written as the union of two proper algebraic subsets.
5. This translates, in algebraic geometry, into the fact that the coordinate ring of an affine algebraic set is an integral domain if and only if the algebraic set is an algebraic variety.
6. It's difficult to find affine algebraic set in a sentence. 用affine algebraic set造句挺难的
7. An irreducible affine algebraic set is also called an "'affine variety "'. ( Many authors use the phrase " affine variety " to refer to any affine algebraic set, irreducible or not)
8. An irreducible affine algebraic set is also called an "'affine variety "'. ( Many authors use the phrase " affine variety " to refer to any affine algebraic set, irreducible or not)
9. If " X " is an affine algebraic set ( irreducible or not ) then the Zariski topology on it is defined simply to be the subspace topology induced by its inclusion into some \ mathbb { A } ^ n.
10. In algebraic geometry, an affine variety ( or, more generally, an affine algebraic set ) is defined as the subset of an affine space that is the set of the common zeros of a set of so-called " polynomial functions over the affine space ".
11. More generally, a polynomial defined over a field " K " is absolutely irreducible if it is irreducible over every algebraic extension of " K ", and an affine algebraic set defined by equations with coefficients in a field " K " is absolutely irreducible if it is not the union of two algebraic sets defined by equations in an algebraically closed extension of " K ".
12. Another application, in algebraic geometry, is that " elimination " realizes the geometric operation of projection of an affine algebraic set into a subspace of the ambient space : with above notation, the ( Zariski closure of ) the projection of the algebraic set defined by the ideal " I " into the " Y "-subspace is defined by the ideal I \ cap K [ Y ].