List questions from ring-homomorphism

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Prove that the map R[x,y]→R[x,y] defined by $x\mapsto x+f(y)$, $y\mapsto y$ is an automorphism of R[x,y].

Published on 19 Jan 2017 - 15:41

429

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On the ring of all real valued functions (continuous)

Published on 22 Jan 2017 - 10:36

254

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Kernel of a ring homomorphism and surjection

Published on 29 Jan 2017 - 14:28

263

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Group and Ring Homomorphisms

Published on 07 Feb 2017 - 17:14

69

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Homomorphism of group rings.

Published on 25 Mar 2026 - 14:22

85

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A question to construct homomorphisms $R \to S$ canonically from homomorphisms $R[X] \to S[X]$.

Published on 10 Feb 2017 - 14:10

139

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Trouble Understanding Hom, Modules, and SES

Published on 19 Feb 2017 - 5:23

1k

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Determine whether the maps are ring homomorphisms

Published on 20 Feb 2017 - 23:51

1.1k

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Prove that the rings $End(\mathbb{Z}^{n})$ and $M_{n}(\mathbb{Z})$ are isomorphic

Published on 21 Feb 2017 - 0:53

394

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Uniqueness of homomorphism

Published on 27 Feb 2017 - 6:53

92

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Ring homomorphism $\pi : \mathbb{Z}_b \to \mathbb{Z}_a$ if $a | b$

Published on 02 Mar 2017 - 2:21

440

Views

Is every jordan homomorphism a ring homomorphism

Published on 25 Mar 2026 - 15:21

336

Views

How to formally prove that every $F$-algebra homomorphism $E\rightarrow E $ is a linear transformation?

Published on 10 Mar 2017 - 19:51

53

Views

Is it possible to get the same extension field E/F of F by using different homomorphisms?

Published on 10 Mar 2017 - 20:31

259

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Show that there exists a unique ring homomorphism such that

Published on 17 Mar 2017 - 9:45

List Question

Prove that the map R[x,y]→R[x,y] defined by $x\mapsto x+f(y)$, $y\mapsto y$ is an automorphism of R[x,y].

On the ring of all real valued functions (continuous)

Kernel of a ring homomorphism and surjection

Group and Ring Homomorphisms

Homomorphism of group rings.

A question to construct homomorphisms $R \to S$ canonically from homomorphisms $R[X] \to S[X]$.

Trouble Understanding Hom, Modules, and SES

Determine whether the maps are ring homomorphisms

Prove that the rings $End(\mathbb{Z}^{n})$ and $M_{n}(\mathbb{Z})$ are isomorphic

Uniqueness of homomorphism

Ring homomorphism $\pi : \mathbb{Z}_b \to \mathbb{Z}_a$ if $a | b$

Is every jordan homomorphism a ring homomorphism

How to formally prove that every $F$-algebra homomorphism $E\rightarrow E $ is a linear transformation?

Is it possible to get the same extension field E/F of F by using different homomorphisms?

Show that there exists a unique ring homomorphism such that

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