Question

$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime

score 14.2k · Answer 1 · 2026-04-08 20:46:26

14.2k

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$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime

Published on 08 Apr 2026 - 20:46

score 174 · Answer 2 · 2026-04-12 17:01:53

174

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Finding some homogeneous generators of an ideal.

Published on 12 Apr 2026 - 17:01

score 82 · Answer 3 · 2026-04-16 02:55:07

82

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Proving that these isomorphisms are the $only$ isomorphisms

Published on 16 Apr 2026 - 2:55

score 226 · Answer 4 · 2026-04-15 16:55:44

226

Views

Show $\Bbb Q[(1 + i)/\sqrt{2}]\cong \Bbb Q [X]/⟨X^4 + 1⟩$ by Kronecker's Theorem

Published on 15 Apr 2026 - 16:55

score 596 · Answer 5 · 2026-04-16 09:08:46

596

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Units in $\mathbb{Z}[\sqrt{d}]$

Published on 16 Apr 2026 - 9:08

score 1.5k · Answer 6 · 2026-04-15 07:11:46

1.5k

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A field is a nonzero commutative ring ...

Published on 15 Apr 2026 - 7:11

score 5.8k · Answer 7 · 2026-04-11 23:06:40

5.8k

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Addition and Multiplication table for Ring/Ideal

Published on 11 Apr 2026 - 23:06

score 464 · Answer 8 · 2026-04-16 04:19:34

464

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Exercise about Krull Dimension/Eisenbud, Exercise 10.1

Published on 16 Apr 2026 - 4:19

score 907 · Answer 9 · 2026-04-13 11:14:42

907

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Maximal Ideals of Matrix Ring

Published on 13 Apr 2026 - 11:14

score 101 · Answer 10 · 2026-04-12 15:07:00

101

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"Filters" of associative rings

Published on 12 Apr 2026 - 15:07

score 1k · Answer 11 · 2026-04-21 20:50:55

1k

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If $a,b$ is an $R$-sequence, then $ax-b$ is prime (Eisenbud, Exercise 10.4)

Published on 21 Apr 2026 - 20:50

score 428 · Answer 12 · 2026-04-10 22:39:46

428

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Properties of $Hom_{\mathbb{Z}}(\mathbb{Q}, \mathbb{Q} )$

Published on 10 Apr 2026 - 22:39

score 1.6k · Answer 13 · 2026-04-13 06:28:54

1.6k

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Is every commutative simple ring a field, even if we don't assume it to be unital a priori?

Published on 13 Apr 2026 - 6:28

score 1.1k · Answer 14 · 2026-04-14 21:31:52

1.1k

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$x \otimes y - y \otimes x \neq 0$ in $I \otimes_{R} I$

Published on 14 Apr 2026 - 21:31

score 97 · Answer 15 · 2026-04-16 14:09:08

97

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Equations in the semiring of f.g. modules

Published on 16 Apr 2026 - 14:09

List Question

$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime

Finding some homogeneous generators of an ideal.

Proving that these isomorphisms are the $only$ isomorphisms

Show $\Bbb Q[(1 + i)/\sqrt{2}]\cong \Bbb Q [X]/⟨X^4 + 1⟩$ by Kronecker's Theorem

Units in $\mathbb{Z}[\sqrt{d}]$

A field is a nonzero commutative ring ...

Addition and Multiplication table for Ring/Ideal

Exercise about Krull Dimension/Eisenbud, Exercise 10.1

Maximal Ideals of Matrix Ring

"Filters" of associative rings

If $a,b$ is an $R$-sequence, then $ax-b$ is prime (Eisenbud, Exercise 10.4)

Properties of $Hom_{\mathbb{Z}}(\mathbb{Q}, \mathbb{Q} )$

Is every commutative simple ring a field, even if we don't assume it to be unital a priori?

$x \otimes y - y \otimes x \neq 0$ in $I \otimes_{R} I$

Equations in the semiring of f.g. modules

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