Question

In any ring $R$ with a multiplicative identity , does every non-unit element belongs to some maximal ideal of $R$ ?

score 239 · Answer 1 · 2015-01-18 15:21:54

239

Views

In any ring $R$ with a multiplicative identity , does every non-unit element belongs to some maximal ideal of $R$ ?

Published on 18 Jan 2015 - 15:21

score 309 · Answer 2 · 2015-01-18 21:58:38

309

Views

$M$ is maximal, $P$ is prime but not maximal

Published on 18 Jan 2015 - 21:58

score 207 · Answer 3 · 2015-01-19 08:13:09

207

Views

Conditions on ideal b for fields or integral domains

Published on 19 Jan 2015 - 8:13

score 1.8k · Answer 4 · 2015-01-19 17:22:48

1.8k

Views

integral ring extension, maximal ideals

Published on 19 Jan 2015 - 17:22

score 1k · Answer 5 · 2015-01-21 16:14:47

1k

Views

Showing the inverse map of a ring homomorphism of a prime ideal is again a prime ideal

Published on 21 Jan 2015 - 16:14

score 1.9k · Answer 6 · 2026-03-29 19:17:33

1.9k

Views

do you need $P$ prime to show that $R/P$ is a PID if $R$ is a PID?

Published on 29 Mar 2026 - 19:17

score 1k · Answer 7 · 2015-01-23 02:30:08

1k

Views

A maximal element of the set of non-principal ideals is prime

Published on 23 Jan 2015 - 2:30

score 1.3k · Answer 8 · 2015-01-24 05:13:45

1.3k

Views

Is annihilator of maximal submodule is a maximal ideal?

Published on 24 Jan 2015 - 5:13

score 842 · Answer 9 · 2026-03-26 01:00:04

842

Views

Flat algebra over a Dedekind domain

Published on 26 Mar 2026 - 1:00

score 1.2k · Answer 10 · 2015-01-27 18:07:46

1.2k

Views

A relation between the Jacobson radicals of a ring and those of a certain quotient ring

Published on 27 Jan 2015 - 18:07

score 1.6k · Answer 11 · 2015-01-28 17:56:01

1.6k

Views

The prime ideals of the ring $K[x]$

Published on 28 Jan 2015 - 17:56

score 242 · Answer 12 · 2015-01-29 19:26:00

242

Views

$I$ is maximal ideal $\implies$ $R/I$ has no proper ideals

Published on 29 Jan 2015 - 19:26

score 50 · Answer 13 · 2015-01-29 22:17:10

50

Views

No such prime ideal contains $I_1+I_2\implies I_1 $ and $I_2$ are relatively prime

Published on 29 Jan 2015 - 22:17

score 1k · Answer 14 · 2015-01-30 15:09:10

1k

Views

For a maximal ideal $M$ of $R$ of a commutative ring $R$ ( not necessarily with unity ) , then is $R/M$ a simple ring ?

Published on 30 Jan 2015 - 15:09

score 650 · Answer 15 · 2015-02-01 12:33:26

650

Views

$V$ is irreducible exactly then when $I(V )$ is a prime ideal

Published on 01 Feb 2015 - 12:33

List Question

In any ring $R$ with a multiplicative identity , does every non-unit element belongs to some maximal ideal of $R$ ?

$M$ is maximal, $P$ is prime but not maximal

Conditions on ideal b for fields or integral domains

integral ring extension, maximal ideals

Showing the inverse map of a ring homomorphism of a prime ideal is again a prime ideal

do you need $P$ prime to show that $R/P$ is a PID if $R$ is a PID?

A maximal element of the set of non-principal ideals is prime

Is annihilator of maximal submodule is a maximal ideal?

Flat algebra over a Dedekind domain

A relation between the Jacobson radicals of a ring and those of a certain quotient ring

The prime ideals of the ring $K[x]$

$I$ is maximal ideal $\implies$ $R/I$ has no proper ideals

No such prime ideal contains $I_1+I_2\implies I_1 $ and $I_2$ are relatively prime

For a maximal ideal $M$ of $R$ of a commutative ring $R$ ( not necessarily with unity ) , then is $R/M$ a simple ring ?

$V$ is irreducible exactly then when $I(V )$ is a prime ideal

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