$K \subset L$ a field extension and $L$ algebraically closed implies that $A$ is the algebraic closure of $K$
158525
Given a field, the field of algebraic elements over it in an algebraically closed field extension is again algebraically closed?
109039
Does this "extension property" for polynomial rings satisfy a universal property?
147200
Given fields $K\subseteq L$, why does $f,g$ relatively prime in $K[x]$ imply relatively prime in $L[x]$?
47537
Open nonempty subset of irreducible variety over $k$ has the same Krull dimension as the whole variety?
48162
Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
22716
$A$ is integrally closed if and only if $A_P$ is integrally closed for all maximal ideals $P$ of $A$.
125962
The set $A'$ is closed in a $T_1$ space
41815
Galois extension of intersection of fields
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
128550
Algebraic field extension and intermediate integral domain
158523
Topology: Proof that a finitely generated cone is closed
55764
Algebraic closure of $\mathbb F_p$
107207
$A\subseteq B\subseteq C$ ring extensions, $A\subseteq C$ finite/finitely-generated $\Rightarrow$ $A\subseteq B$ finite/finitely-generated?
77791
Proving an inclusion related to algebraic sets and interpreting it
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
21578
Showing the minimal polynomial for an element in an extension field is the same as the minimal polynomial of a linear transformation.
100553
Complement of a prime ideal is a subset closed under multiplication, containing 1