Question

Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism

score 872 · Answer 1 · 2026-03-17 21:22:42

872

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Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism

Published on 17 Mar 2026 - 21:22

score 121 · Answer 2 · 2026-03-20 14:18:13

121

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Determine all ring homomorphisms of $\varphi:\mathbb{Z}_{10} \to \mathbb{Z}_{10}$

Published on 20 Mar 2026 - 14:18

score 69 · Answer 3 · 2026-03-22 05:24:45

69

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Is it true that $End_K (K [x],A) \simeq A$?

Published on 22 Mar 2026 - 5:24

score 551 · Answer 4 · 2026-03-24 15:52:48

551

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Find all surjective ring homomorphisms $\phi:\mathbb{R}[x] \rightarrow \mathbb{R}.$

Published on 24 Mar 2026 - 15:52

score 141 · Answer 5 · 2026-03-22 05:45:24

141

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Is Homomorphism equivalent to Field extension?

Published on 22 Mar 2026 - 5:45

score 764 · Answer 6 · 2026-03-20 09:33:13

764

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Let $φ:\mathbb{C[x,y,z]}\to \mathbb{C[t]}$ by $φ(f(x,y,z))=f(t,t^2,t^3)$. Find generators for ker($φ$)

Published on 20 Mar 2026 - 9:33

score 212 · Answer 7 · 2026-03-20 07:11:22

212

Views

Is $\mathbb Z[\sqrt[3]2] \cong \mathbb C$?

Published on 20 Mar 2026 - 7:11

score 383 · Answer 8 · 2026-03-19 16:23:50

383

Views

Unital Ring Homomorphisms Questions

Published on 19 Mar 2026 - 16:23

score 216 · Answer 9 · 2026-03-20 01:57:37

216

Views

Showing that if $ker(\theta) \subseteq A$ (an ideal in R) then $R/A \simeq S/\theta(A)$

Published on 20 Mar 2026 - 1:57

score 537 · Answer 10 · 2026-03-20 06:43:53

537

Views

Every homomorphism $\varphi : F \to R$ from a field $F$ to a nonzero ring $R$ is injective: proof details in Artin

Published on 20 Mar 2026 - 6:43

score 868 · Answer 11 · 2026-03-22 05:55:24

868

Views

Showing a ring homomorphism is an isomorphism

Published on 22 Mar 2026 - 5:55

score 193 · Answer 12 · 2026-03-21 23:46:33

193

Views

Counter-example: If $J$ is prime then $f^{-1} (J) $ is prime. $f$ need not be unital.

Published on 21 Mar 2026 - 23:46

score 303 · Answer 13 · 2026-03-21 21:08:04

303

Views

Finding ring homomorphisms $\mathbb{Z}\to\mathbb{Z}/n\mathbb{Z}$

Published on 21 Mar 2026 - 21:08

score 3.1k · Answer 14 · 2026-03-21 20:56:45

3.1k

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Can there be an onto homomorphism from a ring without unity to a ring with unity?

Published on 21 Mar 2026 - 20:56

score 228 · Answer 15 · 2026-03-22 06:19:09

228

Views

Show that this is a ring homomorphism

Published on 22 Mar 2026 - 6:19

List Question

Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism

Determine all ring homomorphisms of $\varphi:\mathbb{Z}_{10} \to \mathbb{Z}_{10}$

Is it true that $End_K (K [x],A) \simeq A$?

Find all surjective ring homomorphisms $\phi:\mathbb{R}[x] \rightarrow \mathbb{R}.$

Is Homomorphism equivalent to Field extension?

Let $φ:\mathbb{C[x,y,z]}\to \mathbb{C[t]}$ by $φ(f(x,y,z))=f(t,t^2,t^3)$. Find generators for ker($φ$)

Is $\mathbb Z[\sqrt[3]2] \cong \mathbb C$?

Unital Ring Homomorphisms Questions

Showing that if $ker(\theta) \subseteq A$ (an ideal in R) then $R/A \simeq S/\theta(A)$

Every homomorphism $\varphi : F \to R$ from a field $F$ to a nonzero ring $R$ is injective: proof details in Artin

Showing a ring homomorphism is an isomorphism

Counter-example: If $J$ is prime then $f^{-1} (J) $ is prime. $f$ need not be unital.

Finding ring homomorphisms $\mathbb{Z}\to\mathbb{Z}/n\mathbb{Z}$

Can there be an onto homomorphism from a ring without unity to a ring with unity?

Show that this is a ring homomorphism

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