List questions from maximal-and-prime-ideals

Published on 14 Oct 2020 - 15:07

648

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Show that (2) is prime ideal in $\mathbb{Z}[i]$

Published on 14 Oct 2020 - 18:53

178

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Must an abstract $C^*$-algebra that is an integral domain be a field?

Published on 23 Feb 2026 - 4:59

813

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Decomposition of the algebraic variety into irreducible components

Published on 27 Mar 2026 - 2:35

207

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On geometric interpretation of commutative rings

Published on 19 Oct 2020 - 4:40

203

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Maximal ideals of $\mathcal{C}((0,1),\mathbb{R})$

Published on 20 Oct 2020 - 9:04

88

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Theorem 17.5 Gallian: A polynomial generates a maximal ideal if and only if it is irreducible.

Published on 24 Oct 2020 - 22:23

149

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On the factorization of prime ideals of $\mathbb{Z}$ in $\mathbb{Z}[\zeta]$

Published on 26 Mar 2026 - 6:31

376

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Extension of a maximal ideal

Published on 28 Oct 2020 - 9:47

114

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Trying to delete in a sum of ideals: P+I=Q+I so P=Q?

Published on 28 Mar 2026 - 22:31

87

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Let $M$ be the only maximal ideal of the local ring $\Bbb{Z}_{(p)}$, show that $\Bbb{Z}_{(p)}/M$ is isomorphic to $\Bbb{Z}/(p)$.

Published on 28 Mar 2026 - 22:29

59

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Number of prime ideals in Dedekind domain containing a given prime.

Published on 02 Nov 2020 - 2:14

35

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How to understand whether a given ideal is a prime ideal in a Dedekind domain

Published on 27 Mar 2026 - 4:58

57

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Is a modular element of maximal ideal unique if it exists?

Published on 01 Apr 2026 - 1:02

57

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An exercise in Steps in commutative algebra

Published on 04 Nov 2020 - 15:16

List Question

Prove that if $M$ is a maximal ideal and $x \notin M$, then $x+M$ is a unit in $R/M$

Show that (2) is prime ideal in $\mathbb{Z}[i]$

Must an abstract $C^*$-algebra that is an integral domain be a field?

Decomposition of the algebraic variety into irreducible components

On geometric interpretation of commutative rings

Maximal ideals of $\mathcal{C}((0,1),\mathbb{R})$

Theorem 17.5 Gallian: A polynomial generates a maximal ideal if and only if it is irreducible.

On the factorization of prime ideals of $\mathbb{Z}$ in $\mathbb{Z}[\zeta]$

Extension of a maximal ideal

Trying to delete in a sum of ideals: P+I=Q+I so P=Q?

Let $M$ be the only maximal ideal of the local ring $\Bbb{Z}_{(p)}$, show that $\Bbb{Z}_{(p)}/M$ is isomorphic to $\Bbb{Z}/(p)$.

Number of prime ideals in Dedekind domain containing a given prime.

How to understand whether a given ideal is a prime ideal in a Dedekind domain

Is a modular element of maximal ideal unique if it exists?

An exercise in Steps in commutative algebra

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