List questions from ring-homomorphism

Published on 26 Jan 2021 - 11:03

55

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Show that the following maps are (not) ring homomorphisms. Complex Numbers.

Published on 27 Jan 2021 - 17:55

366

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Example to show that $\mathbb Z^3$ is not a quotient of $\mathbb Z[X]$

Published on 30 Jan 2021 - 1:45

69

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Verify $f: \mathbb{Z} ⟶ \mathbb{Z}_{r} \times \mathbb{Z}_{s}$ given by $a ⟶ (ā_r, ā_s)$ is an epimorphism

Published on 30 Jan 2021 - 16:09

582

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A surjective ring homomorphism which is not an isomorphism

Published on 02 Feb 2021 - 4:23

73

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On an Isomorphism of Semigroup Rings via Congruence Classes

Published on 25 Mar 2026 - 8:10

203

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The homomorphic images of ring centers are central (Dummit and Foote Exercise 7.3.16 and related question)

Published on 06 Feb 2021 - 4:44

65

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A problem about ring isomorphism?

Published on 27 Mar 2026 - 0:54

128

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Prove that the kernel is a principal ideal

Published on 27 Feb 2021 - 0:36

87

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Prove $\text{Hom}(K,K)=\{0,id_K\}$ for $K=\mathbb{Q}$

Published on 07 Mar 2021 - 16:56

879

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Prove ${\rm Hom}_\mathbb{Z}(\mathbb{Z}_n,\mathbb{Z}_m)\cong \mathbb{Z}_{m,n}$

Published on 09 Mar 2021 - 0:57

135

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Considering there exists a homomorphism between two rings show that a condition must exist.

Published on 09 Mar 2021 - 20:32

172

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Isomorphism of quotient rings with Cartesian product

Published on 27 Mar 2026 - 2:35

133

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The kernel of an evaluation homomorphism

Published on 17 Mar 2021 - 17:03

41

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Ring homomorphism from $\mathbb{F}[x,y]$ to $\mathbb{F}[u]$

Published on 25 Mar 2026 - 17:37

List Question

Prove or confute the follow proposition

Show that the following maps are (not) ring homomorphisms. Complex Numbers.

Example to show that $\mathbb Z^3$ is not a quotient of $\mathbb Z[X]$

Verify $f: \mathbb{Z} ⟶ \mathbb{Z}_{r} \times \mathbb{Z}_{s}$ given by $a ⟶ (ā_r, ā_s)$ is an epimorphism

A surjective ring homomorphism which is not an isomorphism

On an Isomorphism of Semigroup Rings via Congruence Classes

The homomorphic images of ring centers are central (Dummit and Foote Exercise 7.3.16 and related question)

A problem about ring isomorphism?

Prove that the kernel is a principal ideal

Prove $\text{Hom}(K,K)=\{0,id_K\}$ for $K=\mathbb{Q}$

Prove ${\rm Hom}_\mathbb{Z}(\mathbb{Z}_n,\mathbb{Z}_m)\cong \mathbb{Z}_{m,n}$

Considering there exists a homomorphism between two rings show that a condition must exist.

Isomorphism of quotient rings with Cartesian product

The kernel of an evaluation homomorphism

Ring homomorphism from $\mathbb{F}[x,y]$ to $\mathbb{F}[u]$

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