List questions from ring-homomorphism

Published on 21 Jun 2020 - 17:06

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Isomorphic $K[x]$-modules have equal characteristic polynomials

Published on 22 Jun 2020 - 9:42

72

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Uniqueness of homomorphism -universal property

Published on 02 Jul 2020 - 12:49

317

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List all additive morphisms $f: Z_m \to Z_n$, with $Z_n$ the integers modulo $n$.

Published on 24 Mar 2026 - 22:34

172

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Examples of homomorphisms

Published on 25 Mar 2026 - 6:19

216

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Realizing a module structure with endomorphisms

Published on 07 Jul 2020 - 11:40

87

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Proof Verification: $\text{Hom}(\mathbb Z[x],S)=S$ (as rings)

Published on 07 Jul 2020 - 18:16

338

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Example of non-local homomorphism on local rings

Published on 25 Mar 2026 - 12:25

150

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Does the embedding of $M_{n}(\mathbb C)$ into $M_{2n}(\mathbb R)$ send $GL_n(\mathbb C)$ into $GL_{2n}(\mathbb R)$?

Published on 12 Jul 2020 - 21:51

81

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A good way to describe a kernel of a group homomorphism

Published on 14 Jul 2020 - 21:09

438

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For a polynomial ring, is $f(x) \mapsto f(ax+b)$ an automorphism?

Published on 15 Jul 2020 - 3:09

395

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Kernel of homomorphism $\mathbb{K}[X,Y]\rightarrow \mathbb{K}[t^2,t^3]$, $X\mapsto t^2$, $Y\mapsto t^3$

Published on 20 Jul 2020 - 13:06

64

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Showing $\lambda: A \otimes C^* \rightarrow \text{Hom}(C,A)$ is a morphism of algebras

Published on 25 Mar 2026 - 14:34

74

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Show that $ker(f) = n/k$

Published on 24 Mar 2026 - 17:30

363

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Existence of a ring homomorphism implies characteristic divisibility

Published on 28 Jul 2020 - 22:43

List Question

Finite-Type Algebra Property Under Change of Base

Isomorphic $K[x]$-modules have equal characteristic polynomials

Uniqueness of homomorphism -universal property

List all additive morphisms $f: Z_m \to Z_n$, with $Z_n$ the integers modulo $n$.

Examples of homomorphisms

Realizing a module structure with endomorphisms

Proof Verification: $\text{Hom}(\mathbb Z[x],S)=S$ (as rings)

Example of non-local homomorphism on local rings

Does the embedding of $M_{n}(\mathbb C)$ into $M_{2n}(\mathbb R)$ send $GL_n(\mathbb C)$ into $GL_{2n}(\mathbb R)$?

A good way to describe a kernel of a group homomorphism

For a polynomial ring, is $f(x) \mapsto f(ax+b)$ an automorphism?

Kernel of homomorphism $\mathbb{K}[X,Y]\rightarrow \mathbb{K}[t^2,t^3]$, $X\mapsto t^2$, $Y\mapsto t^3$

Showing $\lambda: A \otimes C^* \rightarrow \text{Hom}(C,A)$ is a morphism of algebras

Show that $ker(f) = n/k$

Existence of a ring homomorphism implies characteristic divisibility

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