Field not algebraic over an intersection but algebraic over each original field
82576
Intersection of two subfields of the Rational Function Field in characteristic $0$
126127
A field extension of prime degree
107370
An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
158525
Given a field, the field of algebraic elements over it in an algebraically closed field extension is again algebraically closed?
29653
Show that $xy=0$ is a variety but not a manifold
134896
Enlightening proof that the algebraic numbers form a field
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
151978
Splitting field of x^3-2 as a simple extension
118874
If $v$ is algebraic over $K(u)$, for some $u\in F$, and $v $ is transcendental over $K$, then $u$ is algebraic over $K(v)$
48962
Show the two fields are not isomorphic
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
71102
Subfields of $\mathbb{C}$ which are connected with induced topology
57515
Similar matrices and field extensions
153589
Integral basis of an extension of number fields
4192
Non-algebraically closed field in which every polynomial of degree $<n$ has a root
158924
Example of composition of two normal field extensions which is not normal.