Show that if $F \subset D \subset E$ then D is a field
28313
Intermediate ring between a field and an algebraic extension.
98474
Show the existence of a certain subgroup of F2
49143
Showing $A \subset B \iff A\cap B=A$
127919
prove that if $E$ is connected and $E \subseteq F \subseteq \overline{E}$, then $F$ is connected.
86317
Show that $F\subset Y$ is closed in $Y$ iff $F=Y\;\cap\;H$ where $H\subset X$ is closed in $X$.
4401
Constructive proof that algebraic numbers form a field
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
122415
How to show every field is a Euclidean Domain.
94365
How to prove that if $D$ is countable, then $f(D)$ is either finite or countable?
41099
If $A \subseteq C$ and $B \subseteq D$ then $A \times B \subseteq C \times D$
17212
The preimage of a subset
76496
Showing that every field is an integral domain.
70959
Prove that a set $E$ is closed iff it's complement $E^{c}$ is open
19202
$\mathbb{F}_{p^d}\subseteq\mathbb{F}_{p^n}$ if and only if $d$ divides $n$
141659
Every field is an integral domain
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible