separable closure造句
例句與造句
- In general one has to use separable closures instead of algebraic closures.
- The separable closure of a field is the separable closure of in an algebraic closure of.
- The separable closure of a field is the separable closure of in an algebraic closure of.
- The separable closure is the full algebraic closure if and only if " K " is a perfect field.
- The separable closure of in an algebraic closure of is simply called the "'separable closure "'of.
- It's difficult to find separable closure in a sentence. 用separable closure造句挺難的
- The separable closure of in an algebraic closure of is simply called the "'separable closure "'of.
- Suppose that such an intermediate extension does exist, and is finite, then, where is the separable closure of in.
- A field extension E \ supseteq F is "'separable "', if is the separable closure of in.
- Thus the set of all elements in separable over forms a subfield of, called the "'separable closure "'of in.
- By definition, is perfect if and only if its separable and algebraic closures coincide ( in particular, the notion of a separable closure is only interesting for imperfect fields ).
- When a field " K " is not separably closed, the weight and coweight lattices of a torus over " K " are defined as the respective lattices over the separable closure.
- Moreover, in characteristic 2 there are additional possibilities arising not from exceptional isogenies but rather from the fact that for simply connected type C ( I . e ., symplectic groups ) there are roots that are divisible ( by 2 ) in the weight lattice; this gives rise to examples whose root system ( over a separable closure of the ground field ) is non-reduced; such examples exist with a split maximal torus and an irreducible non-reduced root system of any positive rank.
- To study all ( closed " subgroups of Gal ( " E " sep / " E " ) and the set of all separable algebraic extensions of " E " ( technically, one only obtains those separable algebraic extensions of " E " that occur as subfields of the " chosen " separable closure " E " sep, but since all separable closures of " E " are isomorphic, choosing a different separable closure would give the same Galois group and thus an " equivalent " set of algebraic extensions ).
- To study all ( closed " subgroups of Gal ( " E " sep / " E " ) and the set of all separable algebraic extensions of " E " ( technically, one only obtains those separable algebraic extensions of " E " that occur as subfields of the " chosen " separable closure " E " sep, but since all separable closures of " E " are isomorphic, choosing a different separable closure would give the same Galois group and thus an " equivalent " set of algebraic extensions ).
- To study all ( closed " subgroups of Gal ( " E " sep / " E " ) and the set of all separable algebraic extensions of " E " ( technically, one only obtains those separable algebraic extensions of " E " that occur as subfields of the " chosen " separable closure " E " sep, but since all separable closures of " E " are isomorphic, choosing a different separable closure would give the same Galois group and thus an " equivalent " set of algebraic extensions ).