Prove $(U \otimes V) \otimes W \cong U \otimes (V \otimes W)$
62123
Proving that Tensor Product is Associative
35564
Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$
52642
Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$
92033
Prove that $g$ is a submanifold: $g (t,u,v) = (t^2,u^2,v^2,\sqrt{2}uv, \sqrt{2}tv,\sqrt{2}tu)$
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
138436
How to prove reflexivity, symmetry and transitivity for the following relation?
53687
Why is $\text{Hom}(V,W)$ the same thing as $V^* \otimes W$?
41520
Prove that $L(V,W)$ forms a vector space
133884
A proof using Yoneda lemma
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
90332
Prove that that $U(n)$ is an abelian group.
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
133238
Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
51898
Show that $\operatorname{Hom}_{R} (R,M) \cong M$