Question

Prove or disprove: The image of a ring homomorphism $\phi:R\to S$ is an ideal in $S$.

score 393 · Answer 1 · 2026-03-25 04:42:31

393

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Prove or disprove: The image of a ring homomorphism $\phi:R\to S$ is an ideal in $S$.

Published on 25 Mar 2026 - 4:42

score 7.3k · Answer 2 · 2018-10-29 07:42:41

7.3k

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Show that following quotient ring is field: $R[x]/(x^2+1)$

Published on 29 Oct 2018 - 7:42

score 258 · Answer 3 · 2026-03-25 01:18:40

258

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Ideals of a Semigroup - Exercise 1.9.19 of Howie's “Fundamentals of Semigroup Theory”.

Published on 25 Mar 2026 - 1:18

score 622 · Answer 4 · 2026-03-25 04:42:37

622

Views

Every subset of ideals of $R$ has maximal element $\implies$ Every ideal of $R$ is finitely generated, if $R$ is Noetherian.

Published on 25 Mar 2026 - 4:42

score 41 · Answer 5 · 2026-03-26 22:16:18

41

Views

Can a finite subset of integers ever be a maximal anti-ideal?

Published on 26 Mar 2026 - 22:16

score 32 · Answer 6 · 2026-03-25 03:03:43

32

Views

Anti-ideals in $\Bbb{Z}$ form a matroid, so all maximal anti-ideals are in bijection?

Published on 25 Mar 2026 - 3:03

score 388 · Answer 7 · 2026-02-23 02:29:17

388

Views

Contraction of (non-prime) ideals in integral extensions

Published on 23 Feb 2026 - 2:29

score 106 · Answer 8 · 2026-03-28 11:53:37

106

Views

Principal non-prime ideal whose extension is prime

Published on 28 Mar 2026 - 11:53

score 4k · Answer 9 · 2018-11-01 23:02:53

4k

Views

$(x,y)\subset \mathbb Q[x,y]$ is not a principal ideal

Published on 01 Nov 2018 - 23:02

score 328 · Answer 10 · 2026-03-25 07:40:25

328

Views

Proving Ascending Ideals Stabilize in PID

Published on 25 Mar 2026 - 7:40

score 59 · Answer 11 · 2018-11-04 18:28:54

59

Views

Let $I$ and $J$ be ideals, $(I+J)/I\subseteq (I+J)$?

Published on 04 Nov 2018 - 18:28

score 13 · Answer 12 · 2026-03-01 12:03:02

13

Views

Prove that for $C_i\in \mathscr{C}$ and $C=\bigcup C_i $ $ C\in \mathscr{C}. \ $ $\mathscr{C}$ is a chain of S

Published on 01 Mar 2026 - 12:03

score 70 · Answer 13 · 2026-03-27 13:42:10

70

Views

Prove that for distinct prime ideals $P, Q$ of PID $R$, $P^n + Q^m = R$.

Published on 27 Mar 2026 - 13:42

score 463 · Answer 14 · 2026-03-25 12:37:37

463

Views

Proving that $\mathbb{Z}/128\mathbb{Z}$ has exactly one maximal ideal?

Published on 25 Mar 2026 - 12:37

score 2k · Answer 15 · 2026-03-25 04:41:42

2k

Views

Proving that an inverse ring homomorphism of an ideal is an ideal?

Published on 25 Mar 2026 - 4:41

List Question

Prove or disprove: The image of a ring homomorphism $\phi:R\to S$ is an ideal in $S$.

Show that following quotient ring is field: $R[x]/(x^2+1)$

Ideals of a Semigroup - Exercise 1.9.19 of Howie's “Fundamentals of Semigroup Theory”.

Every subset of ideals of $R$ has maximal element $\implies$ Every ideal of $R$ is finitely generated, if $R$ is Noetherian.

Can a finite subset of integers ever be a maximal anti-ideal?

Anti-ideals in $\Bbb{Z}$ form a matroid, so all maximal anti-ideals are in bijection?

Contraction of (non-prime) ideals in integral extensions

Principal non-prime ideal whose extension is prime

$(x,y)\subset \mathbb Q[x,y]$ is not a principal ideal

Proving Ascending Ideals Stabilize in PID

Let $I$ and $J$ be ideals, $(I+J)/I\subseteq (I+J)$?

Prove that for $C_i\in \mathscr{C}$ and $C=\bigcup C_i $ $ C\in \mathscr{C}. \ $ $\mathscr{C}$ is a chain of S

Prove that for distinct prime ideals $P, Q$ of PID $R$, $P^n + Q^m = R$.

Proving that $\mathbb{Z}/128\mathbb{Z}$ has exactly one maximal ideal?

Proving that an inverse ring homomorphism of an ideal is an ideal?

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