Question

Building quotient rings

score 139 · Answer 1 · 2014-06-26 09:26:27

139

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Building quotient rings

Published on 26 Jun 2014 - 9:26

score 599 · Answer 2 · 2014-06-30 16:46:04

599

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Structure Theorem for Finite Commutative Rings with unity

Published on 30 Jun 2014 - 16:46

score 947 · Answer 3 · 2014-07-05 03:01:57

947

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

Published on 05 Jul 2014 - 3:01

score 163 · Answer 4 · 2014-08-03 14:16:09

163

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

Published on 03 Aug 2014 - 14:16

score 734 · Answer 5 · 2014-08-06 12:44:01

734

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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 06 Aug 2014 - 12:44

score 128 · Answer 6 · 2014-08-09 16:00:14

$R$ 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 491 · Answer 7 · 2014-08-21 02:37:26

491

Views

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

Published on 21 Aug 2014 - 2:37

score 446 · Answer 8 · 2014-08-27 17:39:28

446

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

Published on 27 Aug 2014 - 17:39

score 472 · Answer 9 · 2014-09-01 06:03:31

472

Views

$R$ 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 01 Sep 2014 - 6:03

score 524 · Answer 10 · 2014-09-16 15:26:27

524

Views

Finite Division Rings are Fields

Published on 16 Sep 2014 - 15:26

score 615 · Answer 11 · 2014-10-01 07:29:31

615

Views

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

Published on 01 Oct 2014 - 7:29

score 222 · Answer 12 · 2014-10-05 13:54:59

222

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finding all rings of order $p^3$

Published on 05 Oct 2014 - 13:54

score 73 · Answer 13 · 2014-10-09 22:52:22

73

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

Published on 09 Oct 2014 - 22:52

score 95 · Answer 14 · 2014-11-12 02:38:17

95

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Is this "sliding window" unique?

Published on 12 Nov 2014 - 2:38

score 242 · Answer 15 · 2014-11-17 04:34:20

242

Views

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

Published on 17 Nov 2014 - 4:34

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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