List questions from ring-isomorphism

Published on 21 Oct 2018 - 11:45

100

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Seeking an isomorphism from $\langle\mathbb{Q},=,<\rangle\to\langle\mathbb{Q}\cap((0,1)\cup(2,3)),=,<\rangle$

Published on 23 Oct 2018 - 17:25

440

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Showing the factor ring $\mathbb Z[x]/\langle x^2 + 1\rangle$ is isomorphic to the Gaussian integers.

Published on 23 Oct 2018 - 20:19

90

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Showing this map is injective

Published on 25 Mar 2026 - 6:00

64

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Relationship between a polynomial and its constant term (ring)

Published on 06 Nov 2018 - 12:32

635

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Showing that if $\Bbb Z/ab\Bbb Z$ is isomorphic to $\Bbb Z/a\Bbb Z \times \Bbb Z/b\Bbb Z$, then $gcd(a,b)=1$ necessarily.

Published on 08 Nov 2018 - 4:25

112

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Ring isomorphic to $\mathbb{Z}[1/3]/(5)$?

Published on 09 Nov 2018 - 0:07

163

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Defining isomorphism of rings

Published on 13 Nov 2018 - 18:02

472

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Showing isomorphism of Quotient Ring to direct product of Complex numbers

Published on 17 Nov 2018 - 22:53

97

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Fundamental ismorphism theorem

Published on 25 Mar 2026 - 9:31

167

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Isomorphic ring $\mathbb{Q}[x]/(x^3+x) \cong \mathbb{Q} \times \mathbb{Q}[x]/(x^2+1)$

Published on 21 Nov 2018 - 11:29

243

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Proof: $ { \mathbb{Q}[x] } / (x^2 +3x +1) \cong \mathbb{Q}(\sqrt{5}) $

Published on 24 Nov 2018 - 23:12

33

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Showing that three rings are isomorphic

Published on 25 Mar 2026 - 1:22

295

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Group ring isomorphic to matrix ring

Published on 25 Mar 2026 - 1:14

178

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Are multiplicative monoids of different rings isomorphic?

Published on 25 Mar 2026 - 1:16

List Question

How to prove isomorphism for rings in Galois Theory?

Seeking an isomorphism from $\langle\mathbb{Q},=,<\rangle\to\langle\mathbb{Q}\cap((0,1)\cup(2,3)),=,<\rangle$

Showing the factor ring $\mathbb Z[x]/\langle x^2 + 1\rangle$ is isomorphic to the Gaussian integers.

Showing this map is injective

Relationship between a polynomial and its constant term (ring)

Showing that if $\Bbb Z/ab\Bbb Z$ is isomorphic to $\Bbb Z/a\Bbb Z \times \Bbb Z/b\Bbb Z$, then $gcd(a,b)=1$ necessarily.

Ring isomorphic to $\mathbb{Z}[1/3]/(5)$?

Defining isomorphism of rings

Showing isomorphism of Quotient Ring to direct product of Complex numbers

Fundamental ismorphism theorem

Isomorphic ring $\mathbb{Q}[x]/(x^3+x) \cong \mathbb{Q} \times \mathbb{Q}[x]/(x^2+1)$

Proof: $ { \mathbb{Q}[x] } / (x^2 +3x +1) \cong \mathbb{Q}(\sqrt{5}) $

Showing that three rings are isomorphic

Group ring isomorphic to matrix ring

Are multiplicative monoids of different rings isomorphic?

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