List questions from ring-homomorphism | MathQa

How would you show that field automorphisms fix prime subfields?

Published on 12 Jan 2025 - 23:21

To show that $\langle x-a , y-b\rangle$ is a maximal ideal of $F[x,y]$ by showing that $F[x,y]/\langle x-a , y-b\rangle$ is a field

Published on 12 Jan 2025 - 23:32

Let $A$ be a ring, $M''$ and $P$ be $A$-modules and $f:P\rightarrow M''$ a homomorphism...

Published on 12 Jan 2025 - 23:22

What does the homomorphism $\rho: \mathbb Z[X] \longrightarrow \mathbb R$, $X\longmapsto 1+\sqrt2$ describe?

Published on 12 Jan 2025 - 23:29

If $R_1$ is a division ring, any nontrivial homomorphism $\phi : R_1 \rightarrow R_2$ is injective

Published on 12 Jan 2025 - 23:28

On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions

Published on 12 Jan 2025 - 23:30

Let K be a field, $b\in K$, does there exist a field L and $c\in L$ with: there is no homomorphism, such as $\phi(b)=c$?

Published on 12 Jan 2025 - 23:31

Prove or Disprove: there is only one ring homomorphism $f:\mathbb{R} \rightarrow \mathbb{C}$

Published on 12 Jan 2025 - 23:27

Problem in solving a question of field homomorphism.

Published on 12 Jan 2025 - 23:12

Ring Homomorphisms of Fields with $f(1)=1$ are Injective?

Published on 12 Jan 2025 - 23:13