purely inseparable extension मीनिंग इन हिंदी

उदाहरण वाक्य

1. Several equivalent and more concrete definitions for the notion of a purely inseparable extension are known.
2. Purely inseparable extensions do occur naturally; for example, they occur in algebraic geometry over fields of prime characteristic.
3. introduced a variation of Galois theory for purely inseparable extensions of exponent 1, where the Galois groups of field automorphisms in Galois theory are replaced by restricted Lie algebras of derivations.
4. The Jacobson Bourbaki theorem implies both the usual Galois correspondence for subfields of a Galois extension, and Jacobson's Galois correspondence for subfields of a purely inseparable extension of exponent at most 1.
5. In characteristic " p ", an isogeny of degree " p " of abelian varieties must, for their function fields, give either an Artin Schreier extension or a purely inseparable extension.
6. The extreme opposite of the concept of separable extension, namely the concept of purely inseparable extension, also occurs quite naturally, as every algebraic extension may be decomposed in a unique way as a purely inseparable extension of separable extension.
7. The extreme opposite of the concept of separable extension, namely the concept of purely inseparable extension, also occurs quite naturally, as every algebraic extension may be decomposed in a unique way as a purely inseparable extension of separable extension.
8. Remark : The same idea in the proof shows that if L / K is a purely inseparable extension ( need not be normal ), then \ operatorname { Spec } B \ to \ operatorname { Spec } A is bijective.
9. The known proofs of this equality use the fact that if K \ supseteq F is a purely inseparable extension, and if is a separable irreducible polynomial in, then remains irreducible in " K " [ " X " ] ).
10. In particular, \ alpha ^ { p } = a and by the property stated in the paragraph directly above, it follows that F [ \ alpha ] \ supseteq F is a non-trivial purely inseparable extension ( in fact, E = F [ \ alpha ], and so E \ supseteq F is automatically a purely inseparable extension ).