List questions from ring-theory

Published on 14 Apr 2026 - 0:32

174

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Show that the rings $R_1=F_5[x]/(x^2)$ and $R_2=F_5\times F_5$ are not isomorphic.

Published on 14 Apr 2026 - 21:28

837

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Why would a field not be considered a discrete valuation ring?

Published on 04 May 2026 - 21:11

328

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$\mathbb{Z}[X]/(2x+4,x^2-3) \cong \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$

Published on 09 Apr 2026 - 20:41

114

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For which countable successor ordinals $\alpha$ is the reverse order isomorphic to the ideals of a PID ordered by inclusion?

Published on 15 Apr 2026 - 17:23

322

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Centralizer of semisimple matrix

Published on 11 Apr 2026 - 0:38

1.5k

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Find all the maximal ideals in the ring $\mathbb{R}[x]$.

Published on 16 Apr 2026 - 0:27

3.4k

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Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID

Published on 14 Apr 2026 - 0:35

114

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On the irreducibility of $x^3+x^2+x+2$ in $\mathbb{Z}/(n)[x]$

Published on 17 Apr 2026 - 7:35

1.8k

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Integral Domain but not a UFD

Published on 10 Apr 2026 - 17:45

589

Views

Boolean algebra gives rise to a ring

Published on 13 Apr 2026 - 11:45

88

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

Published on 17 Apr 2026 - 14:18

136

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Find the ring of homomorphisms $\mathbb{Z} \to \mathbb{Z}$

Published on 11 Apr 2026 - 8:38

2.2k

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Every nilpotent ideal is a nil ideal.

Published on 13 Apr 2026 - 17:12

228

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Splitting of an exact sequence

Published on 14 Apr 2026 - 6:04

List Question

Prove that some canonical homomorphism is injective.

Show that the rings $R_1=F_5[x]/(x^2)$ and $R_2=F_5\times F_5$ are not isomorphic.

Why would a field not be considered a discrete valuation ring?

$\mathbb{Z}[X]/(2x+4,x^2-3) \cong \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$

For which countable successor ordinals $\alpha$ is the reverse order isomorphic to the ideals of a PID ordered by inclusion?

Centralizer of semisimple matrix

Find all the maximal ideals in the ring $\mathbb{R}[x]$.

Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID

On the irreducibility of $x^3+x^2+x+2$ in $\mathbb{Z}/(n)[x]$

Integral Domain but not a UFD

Boolean algebra gives rise to a ring

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

Find the ring of homomorphisms $\mathbb{Z} \to \mathbb{Z}$

Every nilpotent ideal is a nil ideal.

Splitting of an exact sequence

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