If $P_1$ and $P_2$ are coprime, how do I show that $\ker ( (P_1 \times P_2 )(f) )=\ker(P_1 (f)) \oplus \ker(P_2(f))$?
37953
Primary Decomposition of $\mathbb{R^n}$ under T
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
34567
If $G_1$ and $G_2$ are finite group and $H\leq G_1\times G_2$ then $H=P_1\times P_2$ with $P_i\leq G_i$?
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
80892
Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
81238
Is $O(2)$ really not isomorphic to $SO(2)\times \{-1,1\}$?
124844
Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
100361
Show that ord$_{p}2 = 2^{n + 1}$.
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
113411
If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?