List questions from ideals

Published on 01 Jan 2015 - 16:13

2.2k

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Is the complement of a prime ideal closed under both addition and multiplication?

Published on 29 Mar 2026 - 23:59

840

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How to prove that a maximal ideal of a ring is unique?

Published on 29 Mar 2026 - 23:59

105

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On structure of every ideal of the product ring $R_1\times R_2$

Published on 03 Oct 2019 - 2:18

45

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$(A\cap B)/C=A/C\cap B/C$ for ideals?

Published on 03 Oct 2019 - 2:23

52

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Number of roots of a separable polynomial over a connected ring does not exceed deg $f$.

Published on 05 Oct 2019 - 16:49

910

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Does minimal ideal always imply principal ideal?

Published on 06 Oct 2019 - 12:57

43

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Show that $K $ is prime ideal of $K $

Published on 30 Mar 2026 - 0:05

52

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The number of ideals in $\mathcal{O}_K$ whose norm is a prime number $p$ is bounded by $[K:Q]$.

Published on 06 Oct 2019 - 19:52

23

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Noetherian ring is finitely generated

Published on 26 Mar 2026 - 4:29

879

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Irreducible element of $\mathbb{Z}[\sqrt{-d}]$ generating an ideal that isn't prime

Published on 30 Mar 2026 - 0:05

42

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Prove $I=\{r\in R\vert rL\subseteq N\}$ is an ideal of $R$.

Published on 08 Oct 2019 - 14:16

80

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Prove that a certain ideal $I$ of $\mathbb Z [x]$ is not a principal ideal.

Published on 10 Oct 2019 - 20:14

212

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Prove the Example of Multiplication Module

Published on 11 Oct 2019 - 15:39

29

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Internal direct sum of left ideals (as submodules)

Published on 25 Mar 2026 - 15:11

List Question

Is $\{x f(x)+3g(x) \;|\;f,g\in \mathbb{Q}[x]\}$ a (main) ideal?

Is the complement of a prime ideal closed under both addition and multiplication?

How to prove that a maximal ideal of a ring is unique?

On structure of every ideal of the product ring $R_1\times R_2$

$(A\cap B)/C=A/C\cap B/C$ for ideals?

Number of roots of a separable polynomial over a connected ring does not exceed deg $f$.

Does minimal ideal always imply principal ideal?

Show that $K $ is prime ideal of $K $

The number of ideals in $\mathcal{O}_K$ whose norm is a prime number $p$ is bounded by $[K:Q]$.

Noetherian ring is finitely generated

Irreducible element of $\mathbb{Z}[\sqrt{-d}]$ generating an ideal that isn't prime

Prove $I=\{r\in R\vert rL\subseteq N\}$ is an ideal of $R$.

Prove that a certain ideal $I$ of $\mathbb Z [x]$ is not a principal ideal.

Prove the Example of Multiplication Module

Internal direct sum of left ideals (as submodules)

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