19 июл. 2023 г. · The smallest field where every element has an inverse is the field of rational numbers, denoted by ℚ. In this field, every non-zero element 'Q' ...

2 окт. 2022 г. · It is quite exactly what it says on the tin: a field that is algebraically closed and only contains finitely many elements.

12 окт. 2021 г. · What is the smallest algebraically closed field? First off, no finite field (where 0≠1 0 ≠ 1 ) is algebraically closed. For if F={ ...

12 окт. 2021 г. · The splitting field of a polynomial over F is the smallest subfield of the algebraic closure ¯¯¯¯F F ¯ which contains all the roots of that ...

22 июл. 2023 г. · What is the smallest algebraically closed field? First off, no finite field (where 0≠1 0 ≠ 1 ) is algebraically closed. For if F={ ...

9 апр. 2019 г. · What is the smallest algebraically closed field? First off, no finite field (where 0≠1 0 ≠ 1 ) is algebraically closed. For if F={ ...

13 июл. 2019 г. · The main example of an algebraically closed field is the field C C of complex numbers. Any polynomial equation p(z) ...

15 февр. 2018 г. · Every field F has a unique algebraic closure (up to isomorphism); it is the smallest field in which every algebraic equation with coefficients ...

2 авг. 2019 г. · An algebraically closed field is a field F F with the property that any non-constant polynomial with coefficients in F F has a root in F F , and ...

10 апр. 2019 г. · So no. Algebraically closed fields are not “quasi”-finite; they're anything but finite.