List questions from maximal-and-prime-ideals

Published on 11 Aug 2018 - 17:03

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Noncommutative rings and prime/maximal ideals

Published on 25 Mar 2026 - 7:41

105

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Examining $\mathbb{Z}[\sqrt{-3}]_{\mathfrak{p}}\subset \mathbb{Z}[\frac{1+\sqrt{-3}}{2}]_{\mathfrak{p}}$

Published on 25 Mar 2026 - 22:03

453

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Dummit and Foote problem 11 in section 7.4

Published on 16 Aug 2018 - 1:33

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Quotients of powers of maximal ideal in a local ring.

Published on 25 Mar 2026 - 1:17

301

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Find the Jacobson radical of a matrix ring

Published on 25 Mar 2026 - 7:43

58

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Radical of the ideal $I^2$ is a maximal ideal.

Published on 30 Aug 2018 - 21:10

106

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Theorem 10.2 in Matsumura's commutative ring theory

Published on 01 Sep 2018 - 11:02

1.4k

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Every maximal ideal of a commutative unitary ring is prime (Proof explanation)

Published on 02 Sep 2018 - 23:44

30

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(Proof explanation) In integral domain let there be a prime ideal $(a)$ then $a$ is irreducible.

Published on 03 Sep 2018 - 1:02

38

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Is $\sqrt{X-1}$ an element of the completed ring $\mathbb{C}[X]_\mathfrak{p}$ with $\mathfrak{p} = (X+1)$?

Published on 03 Sep 2018 - 11:59

128

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Is $k[x,y]/{(f,g)}$ an integral domain, where $f$ and $g$ are irreducibles?

Published on 06 Sep 2018 - 23:17

42

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Actions of $C^*$-dynamical systems on primitive ideals

Published on 25 Mar 2026 - 13:53

116

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Given a field $F$ and $R=F[x_1,...x_n]$, show the ideal $(x_1,x_2...x_i)$ is a prime ideal for each i

Published on 14 Sep 2018 - 21:00

139

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About the hypotheses for a ring to contain a maximal ideal

Published on 20 Sep 2018 - 8:23

List Question

Maximal ideals are prime ideals in the non-commutative case

Noncommutative rings and prime/maximal ideals

Examining $\mathbb{Z}[\sqrt{-3}]_{\mathfrak{p}}\subset \mathbb{Z}[\frac{1+\sqrt{-3}}{2}]_{\mathfrak{p}}$

Dummit and Foote problem 11 in section 7.4

Quotients of powers of maximal ideal in a local ring.

Find the Jacobson radical of a matrix ring

Radical of the ideal $I^2$ is a maximal ideal.

Theorem 10.2 in Matsumura's commutative ring theory

Every maximal ideal of a commutative unitary ring is prime (Proof explanation)

(Proof explanation) In integral domain let there be a prime ideal $(a)$ then $a$ is irreducible.

Is $\sqrt{X-1}$ an element of the completed ring $\mathbb{C}[X]_\mathfrak{p}$ with $\mathfrak{p} = (X+1)$?

Is $k[x,y]/{(f,g)}$ an integral domain, where $f$ and $g$ are irreducibles?

Actions of $C^*$-dynamical systems on primitive ideals

Given a field $F$ and $R=F[x_1,...x_n]$, show the ideal $(x_1,x_2...x_i)$ is a prime ideal for each i

About the hypotheses for a ring to contain a maximal ideal

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