When does the equality $\mathrm{ht}\:\mathfrak{p}+\mathrm{coht}\:\mathfrak{p}=\dim R$ happen?
103380
Is $\operatorname{height} \mathfrak{p} + \dim A / \mathfrak{p} = \dim A$ true?
17191
How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
133238
Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
90287
How to derive $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$
42355
Double check $G\sim H$ iff $G≈H$
74187
$\operatorname{ord}(u)=r,\,\operatorname{ord}(v)=s$ $\,\Rightarrow\,\operatorname{ord}(uv)=rs\,$ if $\,r,s\,$ (co)primes
146541
Why $\dim U+\dim U^\perp=\dim V$?
6843
Explain $\iint \mathrm dx\,\mathrm dy = \iint r \,\mathrm \,d\alpha\,\mathrm dr$
132595
$\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
20581
How to show that $\Gamma\vdash (\varphi\to\neg\varphi)\to\varphi$?
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
2342
How does equality $\mathfrak{m}^\mathfrak{m} = 2^\mathfrak{m}$ in $\sf{ZF}$ relate to the axiom of choice?
111746
$(A/\mathfrak{a}) \otimes_A M \simeq M / \mathfrak{a}M$ by tensoring the canonical exact sequence.
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
104828
Show that $\cot \frac{\pi}{2m}\cot \frac{2\pi}{2m}\cot \frac{3\pi}{2m}...\cot \frac{(m-1)\pi}{2m}=1$