List questions from ring-theory

Published on 11 Apr 2026 - 3:15

136

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Is it a field or not?

Published on 11 Apr 2026 - 1:21

208

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Principal ideals as generated groups

Published on 09 Apr 2026 - 5:26

45

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A cyclic right ideal which is not finitely generated

Published on 11 Apr 2026 - 11:52

39

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Each $c \in R^*$ divides each polynomial of $R[X]$

Published on 16 Apr 2026 - 15:35

171

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Algebra - Gaussian integers

Published on 18 Apr 2026 - 7:33

270

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How to calculate $\operatorname{Spec} \mathbb{C}[x,y]/(y^2-x^3)$

Published on 22 Apr 2026 - 1:29

118

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Readings for Noether

Published on 22 Apr 2026 - 1:09

235

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If $R$ is a noetherian local ring, then every 2-generated ideal has finite projective dimension iff $R$ is a UFD

Published on 13 Apr 2026 - 20:56

576

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Matsumura, Exercise 18.8: Cohen-Macaulay and (not) Gorenstein

Published on 17 Apr 2026 - 9:48

981

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Suppose a finite ring $R$. Show that each $x \in R$ is exactly one of a unit, nilpotent, or $x^k$ is idempotent

Published on 16 Apr 2026 - 1:11

91

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Give an example of a ring in which there exist $x,y,z \in R\setminus\{1,0\}$ such that $x$ is a unit, $y$ is nilpotent, and $z$ is idempotent.

Published on 14 Apr 2026 - 1:42

241

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Comparing injective dimensions in a short exact sequence

Published on 09 Apr 2026 - 17:49

26

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Is $\min \deg$ in a dirichlet subring interesting or is it always $1$?

Published on 14 Apr 2026 - 14:41

1k

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$\mathbb{Z} _{29}$ is a field. True or False.

Published on 12 Apr 2026 - 6:17

List Question

Brauer Group - A measure of complexity?

Is it a field or not?

Principal ideals as generated groups

A cyclic right ideal which is not finitely generated

Each $c \in R^*$ divides each polynomial of $R[X]$

Algebra - Gaussian integers

How to calculate $\operatorname{Spec} \mathbb{C}[x,y]/(y^2-x^3)$

Readings for Noether

If $R$ is a noetherian local ring, then every 2-generated ideal has finite projective dimension iff $R$ is a UFD

Matsumura, Exercise 18.8: Cohen-Macaulay and (not) Gorenstein

Suppose a finite ring $R$. Show that each $x \in R$ is exactly one of a unit, nilpotent, or $x^k$ is idempotent

Give an example of a ring in which there exist $x,y,z \in R\setminus\{1,0\}$ such that $x$ is a unit, $y$ is nilpotent, and $z$ is idempotent.

Comparing injective dimensions in a short exact sequence

Is $\min \deg$ in a dirichlet subring interesting or is it always $1$?

$\mathbb{Z} _{29}$ is a field. True or False.

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