Prove that : $K(\alpha)=K(\alpha^{2})$ , $K$ commutative field
22430
Equal simple field extensions?
145561
About the additive group and the multiplicative group of a field
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
101164
Show that $B \cong \mathbb Z /2\mathbb Z$ for a Boolean field B
105170
About product of $k$ commutators
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
32965
Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
81040
proof about commutative operators and T-cyclic vectors
133878
Ring of order $p^2$ is commutative.
123044
Commutative matrices are multiples of the identity
79535
Prove that $R$ is a commutative ring if $x^3=x$
142530
Let K be a field, and $I=(XY,(X-Y)Z)⊆K[X,Y,Z]$. Prove that $√I=(XY,XZ,YZ)$.
31722
Prove $-(-a)=a$ using only ordered field axioms
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.