13 июл. 2016 г. · The typical example of algebraically closed fields is C and the typical non-examples are R,Q and arbitrary finite fields.

5 янв. 2014 г. · In general, an algebraic closure of a field K is denoted by ¯K. Typical examples arising in number theory are K=Q, K=Fp(t), K=Qp.

18 янв. 2016 г. · A field extension F⊇K is called algebraic if every element of F satisfies a polynomial with coefficients in K. In particular, for any α∈F, ...

29 апр. 2014 г. · An uncountable algebraically closed field of characteristic p cannot be isomorphic to a countable union of finite fields.

8 авг. 2011 г. · No, there do not exist any finite algebraically closed fields. For suppose K is a finite field; then the polynomial f(x)=1+∏α∈K(x−α)∈K[x].

10 июн. 2013 г. · Let E be an algebraically closed extension field of a field F. Show that the algebraic closure ˉFE of F in E is algebraically closed.

15 мая 2017 г. · The goal is to write a set of axioms that formalize the property of a field to be "algebraically closed". Of all the possible equivalent ...

5 дек. 2015 г. · Over an algebraically closed field the only irreducible polynomials are those of degree 1. They obviously cannot have multiple roots.

10 сент. 2014 г. · A field F is algebraically closed if it has no proper algebraic extensions. Now, given a field k, an algebraic closure of k is an algebraically ...

14 апр. 2017 г. · We say F is algebraically closed if for any polynomial p(x)∈F[x], F contains all the roots of p(x). This can be considered the most extreme form ...