Smallest subfield containing $F$ and $\alpha$
60212
algebraic element over a field
41505
Transcendental Extensions. $F(\alpha)$ isomorphic to $F(x)$
36099
Show that $\|f\|^{2}$ attains a minimum value on the interior of $B$
134159
Smallest value of $a^2 + b^2 + c^2+ d^2$, given values for $(a+b)(c+d)$, $(a+c)(b+d)$, and $(a+d)(b+c)$
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
153542
Fixed Field of $\sigma, \tau$
129476
The trace map in a finite field.
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?
150170
Subrings of fraction fields
115449
Inclusion of Fields whose order is a prime power
74498
Smallest dense subset of $\mathbb{R}$
155125
Every ordered field has a subfield isomorphic to $\mathbb Q$?
136770
Any field that contains the integers contains the rationals as a subfield (Analysis proof)
144394
Order 2 elements in finite characteristic field
111347
Finding an example of field extensions satisfying certain properties
96355
What is the first order axiom characterizing a field having characteristic zero?
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$