Show $[K : F] = [K : E][E : F]$.
31961
Given fields $M/E/F$, why does $[M:F] = [M:E][E:F]$?
38200
Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?
111406
Proving that a definition of e is unique
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
137715
If $[L:K]$ is prime, show that $L/K$ is a simple extension.
109109
Show that $E(XE[X|G])=E[(E[X|G)^2]$
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
44453
Prove that the normalisation of $A=k[X,Y]/(Y^2-X^2-X^3)$ is $k[t]$ where $t=Y/X$ (Reid, Exercise 4.5)
1770
Matrix $M_1 = M(f', \mathcal{B}, \mathcal{B '})$ of $f$
52596
A basis for $k(X)$ regarded as a vector space over $k$
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
37308
Let $f:K\to K$ with $\|f(x)-f(y)\|\geq ||x-y||$ for all $x,y$. Show that equality holds and that $f$ is surjective.
94469
How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?
50552
find functions that $f(m+k)=f(mk-n)$
13253
Prove $f(S \cup T) = f(S) \cup f(T)$