Question

Projective modules over rings without unit

score 738 · Answer 1 · 2012-03-15 11:10:18

738

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Projective modules over rings without unit

Published on 15 Mar 2012 - 11:10

score 10.3k · Answer 2 · 2012-03-19 05:40:15

10.3k

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If $I+J=R$, where $R$ is a commutative rng, prove that $IJ=I\cap J$.

Published on 19 Mar 2012 - 5:40

score 825 · Answer 3 · 2012-03-28 14:45:22

825

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How many commutative rings with exactly one non-zero zero divisor are there?

Published on 28 Mar 2012 - 14:45

score 264 · Answer 4 · 2012-06-30 01:42:04

264

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Is there a domain without unity in which every element is a product?

Published on 30 Jun 2012 - 1:42

score 93 · Answer 5 · 2012-06-30 12:47:08

93

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Are there rngs whose rngs of matrices are commutative?

Published on 30 Jun 2012 - 12:47

score 10.9k · Answer 6 · 2012-07-10 19:57:57

10.9k

Views

A maximal ideal is always a prime ideal?

Published on 10 Jul 2012 - 19:57

score 138 · Answer 7 · 2012-07-26 08:38:16

138

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Does this proof that $2\mathbb{Z}\not\cong 3\mathbb{Z}$ work?

Published on 26 Jul 2012 - 8:38

score 1k · Answer 8 · 2012-07-30 05:29:08

1k

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Theorem of Kaplansky, $R$ is a division ring if every element but one is (right) quasi-invertible.

Published on 30 Jul 2012 - 5:29

score 102 · Answer 9 · 2012-07-31 20:35:21

102

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Equality in rng with no zero divisors.

Published on 31 Jul 2012 - 20:35

score 217 · Answer 10 · 2012-08-01 18:45:46

217

Views

Why is $S/Z$ a domain for the ideal $Z=\{z\in S\mid za=0,\;\forall a\in R\}$ in $S$?

Published on 01 Aug 2012 - 18:45

score 4.2k · Answer 11 · 2012-09-25 10:02:55

4.2k

Views

proof of chinese remainder theorem for ring

Published on 25 Sep 2012 - 10:02

score 459 · Answer 12 · 2012-11-02 19:44:54

459

Views

Is there a name for this ring-like object?

Published on 02 Nov 2012 - 19:44

score 1.7k · Answer 13 · 2012-11-26 04:14:27

1.7k

Views

if $S$ is a ring (possibly without identity) with no proper left ideals, then either $S^2=0$ or $S$ is a division ring.

Published on 26 Nov 2012 - 4:14

score 680 · Answer 14 · 2012-12-13 15:35:00

680

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Is there any non-monoid ring which has no maximal ideal?

Published on 13 Dec 2012 - 15:35

score 233 · Answer 15 · 2013-01-19 14:31:56

233

Views

In a PID without unit an ideal is maximal iff it is prime.

Published on 19 Jan 2013 - 14:31

List Question

Projective modules over rings without unit

If $I+J=R$, where $R$ is a commutative rng, prove that $IJ=I\cap J$.

How many commutative rings with exactly one non-zero zero divisor are there?

Is there a domain without unity in which every element is a product?

Are there rngs whose rngs of matrices are commutative?

A maximal ideal is always a prime ideal?

Does this proof that $2\mathbb{Z}\not\cong 3\mathbb{Z}$ work?

Theorem of Kaplansky, $R$ is a division ring if every element but one is (right) quasi-invertible.

Equality in rng with no zero divisors.

Why is $S/Z$ a domain for the ideal $Z=\{z\in S\mid za=0,\;\forall a\in R\}$ in $S$?

proof of chinese remainder theorem for ring

Is there a name for this ring-like object?

if $S$ is a ring (possibly without identity) with no proper left ideals, then either $S^2=0$ or $S$ is a division ring.

Is there any non-monoid ring which has no maximal ideal?

In a PID without unit an ideal is maximal iff it is prime.

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