Is $A/\varphi^{-1}(\mathfrak{m})\subseteq B/\mathfrak{m}$ an integral extension?
44065
If $B$ is finitely generated as a $k$-algebra, and $\phi:A\to B$ is a $k$-algebra map, is $\phi^{-1}(M)$ maximal for any maximal $M\subset B$?
157597
Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
100134
Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
80295
Field extensions and algebraic/transcendental elements
20581
How to show that $\Gamma\vdash (\varphi\to\neg\varphi)\to\varphi$?
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
51465
New, elegant proofs for $\varphi(p^{k})=p^{k}-p^{k-1}$
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
13732
$||f||_p\to ||f||_\infty$ under general assumptions
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
22890
Is it coherent to extend $\mathbb{R}$ with a reciprocal of $0$?
2342
How does equality $\mathfrak{m}^\mathfrak{m} = 2^\mathfrak{m}$ in $\sf{ZF}$ relate to the axiom of choice?
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
84021
How can we show that $\varphi(a) \neq a +1$ for every $a \in A$?