Does $\langle f(x),x\rangle=\langle g(x),x\rangle$ imply that $f=g$?
118949
If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$
41363
when is f@g not the same as f[g]?
58943
If $f'(x)\le g'(x)$, prove $f(x)\le g(x)$
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
145600
Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
33025
What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
71187
How to prove $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle$,using $[\hat{x},\hat{p}]=i\hbar$?
20503
Meaning of inner product $\langle \vec{r} | \psi(t)\rangle $
121301
What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?
2907
How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
44843
What is the difference between $|0\rangle $ and $0$?
102990
Prove or disprove: $S_{10} = \langle (1,3),(1,2, ... ,10) \rangle$
98352
If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?