Question

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

score 246 · Answer 1 · 2026-04-11 17:27:43

246

Views

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

Published on 11 Apr 2026 - 17:27

score 159 · Answer 2 · 2026-04-16 11:23:45

159

Views

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

Published on 16 Apr 2026 - 11:23

score 790 · Answer 3 · 2026-04-17 08:35:08

790

Views

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

Published on 17 Apr 2026 - 8:35

score 49 · Answer 4 · 2026-04-16 12:14:28

49

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 16 Apr 2026 - 12:14

score 80 · Answer 5 · 2026-04-13 21:40:25

80

Views

Check whether two given given rings are isomorphic

Published on 13 Apr 2026 - 21:40

score 67 · Answer 6 · 2026-04-12 20:45:48

67

Views

How to Prove Isomorphism Between Two Quotient Fields?

Published on 12 Apr 2026 - 20:45

score 1.4k · Answer 7 · 2026-04-15 17:43:18

1.4k

Views

How many rings are there of order 4 up to isomorphism

Published on 15 Apr 2026 - 17:43

score 108 · Answer 8 · 2026-04-16 03:27:23

108

Views

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

Published on 16 Apr 2026 - 3:27

score 260 · Answer 9 · 2026-04-15 10:57:50

260

Views

Show that two rings of matrices are not isomorphic

Published on 15 Apr 2026 - 10:57

score 96 · Answer 10 · 2026-04-15 22:57:22

96

Views

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

Published on 15 Apr 2026 - 22:57

score 80 · Answer 11 · 2026-04-13 12:54:40

80

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 13 Apr 2026 - 12:54

score 74 · Answer 12 · 2026-04-10 09:48:22

74

Views

Homomorphism in Rings

Published on 10 Apr 2026 - 9:48

score 180 · Answer 13 · 2026-04-14 01:55:04

180

Views

Show that there is no isomorphism

Published on 14 Apr 2026 - 1:55

score 110 · Answer 14 · 2026-04-16 16:26:13

110

Views

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

Published on 16 Apr 2026 - 16:26

score 245 · Answer 15 · 2026-04-10 16:32:28

245

Views

Extending Isomorphisms

Published on 10 Apr 2026 - 16:32

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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