29 апр. 2020 г. · There are two parts to the statement: (1) C is algebraically closed; (2) C is the smallest such field. (2) should be pretty straightforward ...

16 февр. 2012 г. · The former is the smallest algebraically closed field of char. zero, while C is huge in comparison.

7 февр. 2018 г. · The algebraic closure A of Q is the field of algebraic numbers, which consists of those complex numbers which are roots of some non-zero polynomial in one ...

19 янв. 2013 г. · C is the smallest algebraically closed field containing R · 1 · Puiseux series over a non algebraically closed field. 1 · Is an intersection of ...

21 мая 2018 г. · Existence of algebraically closed and algebraic field over another field · 0 · C is the smallest algebraically closed field containing R · 7.

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.

26 июл. 2014 г. · The set of algebraic numbers is the smallest algebraically closed subset of C. ... C is the smallest algebraically closed field containing R · 2.

25 июл. 2014 г. · @user64494 If x∈K and y∈L, where K and L are small, then x+y,xy∈⟨K,L⟩, which I showed was a small field. So K is closed under addition and ...

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.

6 сент. 2016 г. · Note that Kω may be algebraically closed, even though K isn't. For a simple example, set K=R and n ...