Question

How to show that $\mathbb{Z}/13\mathbb{Z}$ is isomorphic to $\mathbb{Z}[i]/(3-2i)$?

score 243 · Answer 1 · 2018-04-11 16:43:37

243

Views

How to show that $\mathbb{Z}/13\mathbb{Z}$ is isomorphic to $\mathbb{Z}[i]/(3-2i)$?

Published on 11 Apr 2018 - 16:43

score 157 · Answer 2 · 2026-03-25 03:03:00

157

Views

Why is there no subring of the integers modulo 29 isomorphic to the integers modulo 8?

Published on 25 Mar 2026 - 3:03

score 788 · Answer 3 · 2026-03-25 03:20:40

788

Views

Why is $\mathbb{Z}[x]/(2, (x^3+1))\cong \mathbb{F}_2[x] /(x^3+1) $?

Published on 25 Mar 2026 - 3:20

score 46 · Answer 4 · 2018-05-07 09:57:51

46

Views

Prove that if $x^2 +\bar ax +\bar 1$ has a double root, then $(\mathbb Z/5)[x]/I$ $\cong$ $(\mathbb Z/5)[x]/(x^2)$ where I = $x^2 +\bar ax +\bar 1$

Published on 07 May 2018 - 9:57

score 77 · Answer 5 · 2018-05-23 09:31:48

77

Views

Check whether two given given rings are isomorphic

Published on 23 May 2018 - 9:31

score 64 · Answer 6 · 2018-05-28 07:46:41

64

Views

How to Prove Isomorphism Between Two Quotient Fields?

Published on 28 May 2018 - 7:46

score 1.4k · Answer 7 · 2018-06-08 18:41:02

1.4k

Views

How many rings are there of order 4 up to isomorphism

Published on 08 Jun 2018 - 18:41

score 105 · Answer 8 · 2018-07-03 01:56:19

105

Views

$A\times B\simeq C\times D \implies A\simeq C\text{ or } A\simeq D$

Published on 03 Jul 2018 - 1:56

score 257 · Answer 9 · 2018-07-07 19:56:27

257

Views

Show that two rings of matrices are not isomorphic

Published on 07 Jul 2018 - 19:56

score 93 · Answer 10 · 2018-07-13 19:38:27

93

Views

Lifting $\overline{\mathbb{Q}}_{p}$-algebra isomorphism to $\overline{\mathbb{Z}}_{p}$-algebra isomorphism

Published on 13 Jul 2018 - 19:38

score 78 · Answer 11 · 2026-03-25 08:12:53

78

Views

If $A= \mathbb{Z}[X]/(X^n+1)$, is it true that $A/mA \cong \mathbb{Z}_m[X]/(X^n+1)$?

Published on 25 Mar 2026 - 8:12

score 69 · Answer 12 · 2018-08-20 09:18:10

69

Views

Homomorphism in Rings

Published on 20 Aug 2018 - 9:18

score 176 · Answer 13 · 2018-10-02 17:58:40

176

Views

Show that there is no isomorphism

Published on 02 Oct 2018 - 17:58

score 107 · Answer 14 · 2018-10-08 13:17:00

107

Views

Show that $\mathbb{Q}[X]/\langle X^3+X\rangle\cong \mathbb{Q} \times \mathbb{Q}[i]$

Published on 08 Oct 2018 - 13:17

score 240 · Answer 15 · 2018-10-16 22:22:25

240

Views

Extending Isomorphisms

Published on 16 Oct 2018 - 22:22

List Question

How to show that $\mathbb{Z}/13\mathbb{Z}$ is isomorphic to $\mathbb{Z}[i]/(3-2i)$?

Why is there no subring of the integers modulo 29 isomorphic to the integers modulo 8?

Why is $\mathbb{Z}[x]/(2, (x^3+1))\cong \mathbb{F}_2[x] /(x^3+1) $?

Prove that if $x^2 +\bar ax +\bar 1$ has a double root, then $(\mathbb Z/5)[x]/I$ $\cong$ $(\mathbb Z/5)[x]/(x^2)$ where I = $x^2 +\bar ax +\bar 1$

Check whether two given given rings are isomorphic

How to Prove Isomorphism Between Two Quotient Fields?

How many rings are there of order 4 up to isomorphism

$A\times B\simeq C\times D \implies A\simeq C\text{ or } A\simeq D$

Show that two rings of matrices are not isomorphic

Lifting $\overline{\mathbb{Q}}_{p}$-algebra isomorphism to $\overline{\mathbb{Z}}_{p}$-algebra isomorphism

If $A= \mathbb{Z}[X]/(X^n+1)$, is it true that $A/mA \cong \mathbb{Z}_m[X]/(X^n+1)$?

Homomorphism in Rings

Show that there is no isomorphism

Show that $\mathbb{Q}[X]/\langle X^3+X\rangle\cong \mathbb{Q} \times \mathbb{Q}[i]$

Extending Isomorphisms

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