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Q about 2nd isomorphism Th for rings: Is this true $(S+I)/I\cong S/(S\cap I)\cong S/I$, for subring $S$ and ideal $I$?

score 81 · Answer 1 · 2020-05-09 15:14:47

81

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Q about 2nd isomorphism Th for rings: Is this true $(S+I)/I\cong S/(S\cap I)\cong S/I$, for subring $S$ and ideal $I$?

Published on 09 May 2020 - 15:14

score 67 · Answer 2 · 2020-05-16 20:17:05

67

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Isomorphic finite rings?

Published on 16 May 2020 - 20:17

score 156 · Answer 3 · 2020-05-17 18:22:26

156

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Ring which isn't isomorphic to any subring of End(V) for any vector space V

Published on 17 May 2020 - 18:22

score 90 · Answer 4 · 2020-05-25 10:30:44

90

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Prove that field $\mathbb{Z}[x]/(x,3)$ is isomorphic to field $\mathbb{Z}/3\mathbb{Z}$.

Published on 25 May 2020 - 10:30

score 124 · Answer 5 · 2026-03-25 06:03:36

124

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Is the ring $3\mathbb Z$ a ring homomorphic image of the ring $2\mathbb Z$.

Published on 25 Mar 2026 - 6:03

score 103 · Answer 6 · 2020-05-27 13:42:18

103

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Are $F_2[x]/\langle x^2\rangle$ and $F_2[x]/\langle x^2+x\rangle$ isomorphic?

Published on 27 May 2020 - 13:42

score 69 · Answer 7 · 2026-03-26 01:02:40

69

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Is there any way to visualize Ring structure using Cayley digraph?

Published on 26 Mar 2026 - 1:02

score 66 · Answer 8 · 2020-05-29 15:21:57

66

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Clarification about Quotient Ring Isomorphism Theorem for a Principal Ideal

Published on 29 May 2020 - 15:21

score 59 · Answer 9 · 2026-03-25 23:36:51

59

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$(\mathbb{Z}/18\mathbb{Z})/(6\mathbb{Z}/18\mathbb{Z})\cong\mathbb{Z}/6\mathbb{Z}$ Proof

Published on 25 Mar 2026 - 23:36

score 36 · Answer 10 · 2026-03-25 18:57:51

36

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How to prove that $(\Bbb{Z}[t]+t\Bbb{R}[t])/t\Bbb{R}[t]\cong\Bbb{Z}\cong\Bbb{Z}[t]/t\Bbb{Z}[t]\cong\Bbb{Z}[t]/(\Bbb{Z}[t]\cap t\Bbb{R}[t])$?

Published on 25 Mar 2026 - 18:57

score 45 · Answer 11 · 2026-03-25 18:57:45

45

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For which ideal $I$ of $\Bbb Z[t]$ is $\mathbb{Z}[t]/I\cong\Bbb Z_{11}$?

Published on 25 Mar 2026 - 18:57

score 153 · Answer 12 · 2020-06-04 05:24:01

153

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Procedure to find explicit isomorphisms between two quotient rings: $\mathbb{R}[x]/(x^2 + 1) \cong \mathbb{R}[x]/(x^2 + \alpha^2)$

Published on 04 Jun 2020 - 5:24

score 87 · Answer 13 · 2020-06-08 21:06:49

87

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Is the function $\phi:\Bbb C\to\Bbb C$ given by $\phi(z)=\bar{z}$ a ring isomorphism (where $\bar{z}$ is the complex conjugate of $z$).

Published on 08 Jun 2020 - 21:06

score 333 · Answer 14 · 2020-06-15 11:21:55

333

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Are fields $Q[x]/(x^2 -5)$ and $Q[x]/(x^2 + 5)$ isomorphic to each other?

Published on 15 Jun 2020 - 11:21

score 97 · Answer 15 · 2020-06-15 12:04:19

97

Views

Are the fields $\Bbb Q[x]/(x^2−5)$ and $\Bbb Q[x]/(x^2+5)$ isomorphic to each other?

Published on 15 Jun 2020 - 12:04

List Question

Q about 2nd isomorphism Th for rings: Is this true $(S+I)/I\cong S/(S\cap I)\cong S/I$, for subring $S$ and ideal $I$?

Isomorphic finite rings?

Ring which isn't isomorphic to any subring of End(V) for any vector space V

Prove that field $\mathbb{Z}[x]/(x,3)$ is isomorphic to field $\mathbb{Z}/3\mathbb{Z}$.

Is the ring $3\mathbb Z$ a ring homomorphic image of the ring $2\mathbb Z$.

Are $F_2[x]/\langle x^2\rangle$ and $F_2[x]/\langle x^2+x\rangle$ isomorphic?

Is there any way to visualize Ring structure using Cayley digraph?

Clarification about Quotient Ring Isomorphism Theorem for a Principal Ideal

$(\mathbb{Z}/18\mathbb{Z})/(6\mathbb{Z}/18\mathbb{Z})\cong\mathbb{Z}/6\mathbb{Z}$ Proof

How to prove that $(\Bbb{Z}[t]+t\Bbb{R}[t])/t\Bbb{R}[t]\cong\Bbb{Z}\cong\Bbb{Z}[t]/t\Bbb{Z}[t]\cong\Bbb{Z}[t]/(\Bbb{Z}[t]\cap t\Bbb{R}[t])$?

For which ideal $I$ of $\Bbb Z[t]$ is $\mathbb{Z}[t]/I\cong\Bbb Z_{11}$?

Procedure to find explicit isomorphisms between two quotient rings: $\mathbb{R}[x]/(x^2 + 1) \cong \mathbb{R}[x]/(x^2 + \alpha^2)$

Is the function $\phi:\Bbb C\to\Bbb C$ given by $\phi(z)=\bar{z}$ a ring isomorphism (where $\bar{z}$ is the complex conjugate of $z$).

Are fields $Q[x]/(x^2 -5)$ and $Q[x]/(x^2 + 5)$ isomorphic to each other?

Are the fields $\Bbb Q[x]/(x^2−5)$ and $\Bbb Q[x]/(x^2+5)$ isomorphic to each other?

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