Question

Building quotient rings

score 141 · Answer 1 · 2026-03-31 22:55:09

141

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Building quotient rings

Published on 31 Mar 2026 - 22:55

score 600 · Answer 2 · 2026-02-23 04:52:43

600

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Structure Theorem for Finite Commutative Rings with unity

Published on 23 Feb 2026 - 4:52

score 948 · Answer 3 · 2026-02-23 04:57:43

948

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Any finite ring is a direct sum of rings of prime power order

Published on 23 Feb 2026 - 4:57

score 164 · Answer 4 · 2026-02-23 04:59:07

164

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When a finite local ring $R$ has $-1$ as a square in $R^\times$?

Published on 23 Feb 2026 - 4:59

score 735 · Answer 5 · 2026-02-23 04:59:35

735

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How to characterize all finite commutative local rings with the maximal ideal of fixed order (if the order is small)?

Published on 23 Feb 2026 - 4:59

score 129 · Answer 6 · 2026-02-23 04:59:34

$R$ is a ring. $(R,+)\cong(Z_2\oplus Z_4,+)$, indecomposable, $\nexists$ 1, noncommutative, has an idempotent $e\neq 0$. Show that $2e\neq 0$.

score 492 · Answer 7 · 2026-02-23 04:55:06

492

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Why is $1 + 1 = 0$ in $\{0, 1\}$ (binary field) and not 1 or 2?

Published on 23 Feb 2026 - 4:55

score 447 · Answer 8 · 2026-02-23 04:56:34

447

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Finite rings without unity that are subrings of finite rings with unity

Published on 23 Feb 2026 - 4:56

score 483 · Answer 9 · 2026-04-07 20:21:14

483

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$R$ be a ring without identity. If $R$ has a maximal left ideal, then the Jacobson radical is still the intersection of all the maximal left ideals?

Published on 07 Apr 2026 - 20:21

score 526 · Answer 10 · 2026-04-01 04:18:23

526

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Finite Division Rings are Fields

Published on 01 Apr 2026 - 4:18

score 616 · Answer 11 · 2026-02-23 04:55:25

616

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Let $A$ a finite ring. Prove that $A$ is a field, or $A$ has zero divisors.

Published on 23 Feb 2026 - 4:55

score 224 · Answer 12 · 2026-04-01 07:00:52

224

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finding all rings of order $p^3$

Published on 01 Apr 2026 - 7:00

score 74 · Answer 13 · 2026-02-23 04:53:35

74

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A finite ring with $p^3$ elements satisfying some condition is local

Published on 23 Feb 2026 - 4:53

score 97 · Answer 14 · 2026-04-01 02:11:11

97

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Is this "sliding window" unique?

Published on 01 Apr 2026 - 2:11

score 243 · Answer 15 · 2026-02-23 04:53:22

243

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Is every finite ring a matrix algebra over a commutative ring?

Published on 23 Feb 2026 - 4:53

List Question

Building quotient rings

Structure Theorem for Finite Commutative Rings with unity

Any finite ring is a direct sum of rings of prime power order

When a finite local ring $R$ has $-1$ as a square in $R^\times$?

How to characterize all finite commutative local rings with the maximal ideal of fixed order (if the order is small)?

$R$ is a ring. $(R,+)\cong(Z_2\oplus Z_4,+)$, indecomposable, $\nexists$ 1, noncommutative, has an idempotent $e\neq 0$. Show that $2e\neq 0$.

Why is $1 + 1 = 0$ in $\{0, 1\}$ (binary field) and not 1 or 2?

Finite rings without unity that are subrings of finite rings with unity

$R$ be a ring without identity. If $R$ has a maximal left ideal, then the Jacobson radical is still the intersection of all the maximal left ideals?

Finite Division Rings are Fields

Let $A$ a finite ring. Prove that $A$ is a field, or $A$ has zero divisors.

finding all rings of order $p^3$

A finite ring with $p^3$ elements satisfying some condition is local

Is this "sliding window" unique?

Is every finite ring a matrix algebra over a commutative ring?

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