Question

Projective modules over rings without unit

score 741 · Answer 1 · 2026-04-14 04:31:57

741

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Projective modules over rings without unit

Published on 14 Apr 2026 - 4:31

score 10.3k · Answer 2 · 2026-04-15 00:33:01

10.3k

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

Published on 15 Apr 2026 - 0:33

score 828 · Answer 3 · 2026-04-11 16:03:09

828

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

Published on 11 Apr 2026 - 16:03

score 267 · Answer 4 · 2026-04-12 03:26:29

267

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

Published on 12 Apr 2026 - 3:26

score 96 · Answer 5 · 2026-04-11 04:30:58

96

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Are there rngs whose rngs of matrices are commutative?

Published on 11 Apr 2026 - 4:30

score 10.9k · Answer 6 · 2026-04-14 01:09:00

10.9k

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A maximal ideal is always a prime ideal?

Published on 14 Apr 2026 - 1:09

score 141 · Answer 7 · 2026-04-10 03:14:07

141

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

Published on 10 Apr 2026 - 3:14

score 1k · Answer 8 · 2026-04-13 08:06:08

1k

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

Published on 13 Apr 2026 - 8:06

score 106 · Answer 9 · 2026-04-16 13:45:23

106

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Equality in rng with no zero divisors.

Published on 16 Apr 2026 - 13:45

score 220 · Answer 10 · 2026-04-13 02:48:43

220

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

Published on 13 Apr 2026 - 2:48

score 4.2k · Answer 11 · 2026-04-11 10:31:17

4.2k

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proof of chinese remainder theorem for ring

Published on 11 Apr 2026 - 10:31

score 462 · Answer 12 · 2026-04-12 12:44:47

462

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Is there a name for this ring-like object?

Published on 12 Apr 2026 - 12:44

score 1.7k · Answer 13 · 2026-04-16 03:32:16

1.7k

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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 16 Apr 2026 - 3:32

score 683 · Answer 14 · 2026-04-13 20:16:15

683

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

Published on 13 Apr 2026 - 20:16

score 236 · Answer 15 · 2026-04-12 09:55:03

236

Views

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

Published on 12 Apr 2026 - 9:55

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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