List questions from ring-isomorphism

Published on 10 Apr 2026 - 0:19

103

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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 16 Apr 2026 - 20:59

443

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

Published on 16 Apr 2026 - 2:18

93

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Showing this map is injective

Published on 15 Apr 2026 - 9:13

67

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Relationship between a polynomial and its constant term (ring)

Published on 10 Apr 2026 - 10:10

638

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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 15 Apr 2026 - 21:44

115

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

Published on 14 Apr 2026 - 21:15

166

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Defining isomorphism of rings

Published on 10 Apr 2026 - 8:08

475

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Showing isomorphism of Quotient Ring to direct product of Complex numbers

Published on 15 Apr 2026 - 6:14

99

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Fundamental ismorphism theorem

Published on 10 Apr 2026 - 23:24

170

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

Published on 17 Apr 2026 - 2:03

245

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

Published on 17 Apr 2026 - 10:13

35

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Showing that three rings are isomorphic

Published on 14 Apr 2026 - 1:02

298

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Group ring isomorphic to matrix ring

Published on 15 Apr 2026 - 13:58

180

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Are multiplicative monoids of different rings isomorphic?

Published on 13 Apr 2026 - 9:02

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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