List questions from maximal-and-prime-ideals

Published on 12 Apr 2026 - 7:22

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Noncommutative rings and prime/maximal ideals

Published on 10 May 2026 - 17:36

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

Published on 10 May 2026 - 16:33

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Dummit and Foote problem 11 in section 7.4

Published on 10 Apr 2026 - 8:18

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Quotients of powers of maximal ideal in a local ring.

Published on 10 May 2026 - 13:50

304

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Find the Jacobson radical of a matrix ring

Published on 10 May 2026 - 17:37

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

Published on 11 Apr 2026 - 2:41

109

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Theorem 10.2 in Matsumura's commutative ring theory

Published on 15 Apr 2026 - 5:33

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

Published on 11 Apr 2026 - 5:16

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

Published on 17 Apr 2026 - 6:11

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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 16 Apr 2026 - 4:46

131

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

Published on 14 Apr 2026 - 4:42

44

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

Published on 12 Apr 2026 - 20:53

119

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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 16 Apr 2026 - 2:56

142

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About the hypotheses for a ring to contain a maximal ideal

Published on 10 Apr 2026 - 16:17

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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