1. This in turn implies that all finite extensions are algebraic. 2. A finitely generated extension may not be a finite extension . 3. Let L / K be a finite extension . 4. For any finite extension of fields, the restriction of scalars takes quasiprojective varieties to quasiprojective varieties. 5. :Elliptic curves are mathematical objects of certain forms defined over a finite extensions of prime fields. 6. This means that the boundary must either come from nowhere or the whole future ends at some finite extension . 7. If E \ supseteq F is a finite extension , its degree is the product of the degrees and. 8. In particular, an algebraic integer is an integral element of a finite extension K / \ mathbb { Q }. 9. Let L be a finite extension of the global field K . We define L / K as the global extension. 10. When it is a finite extension , this is a finite group of order equal to the degree of the extension.
