Question

Showing given map is a ring homomorphism

score 102 · Answer 1 · 2020-07-30 19:58:50

102

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Showing given map is a ring homomorphism

Published on 30 Jul 2020 - 19:58

score 846 · Answer 2 · 2016-08-27 10:58:30

846

Views

Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?

Published on 27 Aug 2016 - 10:58

score 494 · Answer 3 · 2016-08-28 06:37:52

494

Views

$R$ is a subring of $A$ which is a subring of $R[x,y]$ then does there exist an ideal $J$ of $A$ such that $A/J$ and $R$ are ring isomorphic?

Published on 28 Aug 2016 - 6:37

score 138 · Answer 4 · 2026-03-25 11:04:55

138

Views

$C$ be a subring of $B$ which is again a subring of $A$ , let $A,B,C$ be Noetherian and $A \cong C$ , then is $A \cong B$?

Published on 25 Mar 2026 - 11:04

score 226 · Answer 5 · 2016-08-29 11:22:10

226

Views

Are the rings $\mathbb C[x,y]/\langle x^2+y^2-1 \rangle$ and $\mathbb C[x,y]/\langle xy-1 \rangle$ isomorphic ?

Published on 29 Aug 2016 - 11:22

score 89 · Answer 6 · 2026-02-23 08:42:20

89

Views

$R$ be a commutative ring with unity , $|R^{\times}|=p$ an odd prime then is $R$ isomorphic to a quotient of $\mathbb Z_2[x]/\langle x^p-1\rangle$?

Published on 23 Feb 2026 - 8:42

score 375 · Answer 7 · 2016-09-16 20:45:21

375

Views

How do I prove that the determinant map is a ring homomorphism

Published on 16 Sep 2016 - 20:45

score 96 · Answer 8 · 2016-09-23 20:36:31

96

Views

Show that if $F$ is a field and $R$ a non-zero ring, then any homomorphism $\varphi:F\to R$ is injective

Published on 23 Sep 2016 - 20:36

score 116 · Answer 9 · 2016-09-27 21:10:21

116

Views

Is the following an inner automorphism?

Published on 27 Sep 2016 - 21:10

score 2.9k · Answer 10 · 2016-10-15 04:15:54

2.9k

Views

How many distinct ring homomorphisms are there from Z to Z? From Z x Z to Z?

Published on 15 Oct 2016 - 4:15

score 81 · Answer 11 · 2016-11-03 16:25:47

81

Views

Can I prove a set with operations is a ring via a ring homomorphism?

Published on 03 Nov 2016 - 16:25

score 1.1k · Answer 12 · 2016-11-08 07:15:59

1.1k

Views

How to "Visualize" Ring Homomorphisms/Isomorphisms?

Published on 08 Nov 2016 - 7:15

score 651 · Answer 13 · 2016-11-08 18:26:49

651

Views

Prove Ring Homomorphism is One-to-One

Published on 08 Nov 2016 - 18:26

score 362 · Answer 14 · 2016-11-09 02:35:19

362

Views

construct a ring homomorphism

Published on 09 Nov 2016 - 2:35

score 830 · Answer 15 · 2016-11-12 16:49:25

830

Views

Show that there exists a ring homomorphism $f: Z/(m)\rightarrow Z/(n)$ sending 1 to 1 if and only if $n|m$.

Published on 12 Nov 2016 - 16:49

List Question

Showing given map is a ring homomorphism

Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?

$R$ is a subring of $A$ which is a subring of $R[x,y]$ then does there exist an ideal $J$ of $A$ such that $A/J$ and $R$ are ring isomorphic?

$C$ be a subring of $B$ which is again a subring of $A$ , let $A,B,C$ be Noetherian and $A \cong C$ , then is $A \cong B$?

Are the rings $\mathbb C[x,y]/\langle x^2+y^2-1 \rangle$ and $\mathbb C[x,y]/\langle xy-1 \rangle$ isomorphic ?

$R$ be a commutative ring with unity , $|R^{\times}|=p$ an odd prime then is $R$ isomorphic to a quotient of $\mathbb Z_2[x]/\langle x^p-1\rangle$?

How do I prove that the determinant map is a ring homomorphism

Show that if $F$ is a field and $R$ a non-zero ring, then any homomorphism $\varphi:F\to R$ is injective

Is the following an inner automorphism?

How many distinct ring homomorphisms are there from Z to Z? From Z x Z to Z?

Can I prove a set with operations is a ring via a ring homomorphism?

How to "Visualize" Ring Homomorphisms/Isomorphisms?

Prove Ring Homomorphism is One-to-One

construct a ring homomorphism

Show that there exists a ring homomorphism $f: Z/(m)\rightarrow Z/(n)$ sending 1 to 1 if and only if $n|m$.

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