List questions from ring-theory

Published on 13 Apr 2026 - 22:57

198

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surjectivity condition for induced map of prime ideals

Published on 11 May 2026 - 8:27

180

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Let $I = (2,x)$, an ideal in $\mathbb{Z}[x]$. Show there is an element of $II$ not of the form $ab$, where $a, b \in I$.

Published on 14 Apr 2026 - 5:39

259

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Understanding the localization of a module

Published on 27 Mar 2026 - 23:57

101

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Computing projective dimension over hereditary rings (modules).

Published on 15 Apr 2026 - 7:44

78

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Graded Rings , divided polynomial algebra

Published on 10 May 2026 - 16:08

88

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Why is the boolean "OR" operator denoted as "+"?

Published on 09 Apr 2026 - 5:33

127

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A problem regarding a maximal ideal in a polynomial ring in several variables

Published on 14 Apr 2026 - 11:46

658

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$\mathbb Z [x]$ module structure on $\mathbb Z$

Published on 12 Apr 2026 - 17:50

930

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Prove: $R$ is local $\iff$ $R$ has exactly one maximal ideal.

Published on 11 May 2026 - 8:36

222

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$R$ be local and suppose $x ∈ R$ satisfies $x^2 = x$

Published on 11 May 2026 - 8:36

356

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Prove that $x−1$ and $y−1$ are irreducible in $R$

Published on 14 Apr 2026 - 15:27

40

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Show $2$ is not prime in $\{f\in\mathbb{Q}[x]:f(m)\in\mathbb{Z}\text{ for all }m\in\mathbb{N}\}$

Published on 15 Apr 2026 - 9:59

45

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Arithmetic of quotients

Published on 15 Apr 2026 - 19:53

77

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For which $n$ is $\sum_{i=0}^n x^i\in\mathbb{Q}[x]$ irreducible?

Published on 15 Apr 2026 - 17:23

List Question

How to finish this argument showing preimage of maximal ideal is maximal under surjective map.

surjectivity condition for induced map of prime ideals

Let $I = (2,x)$, an ideal in $\mathbb{Z}[x]$. Show there is an element of $II$ not of the form $ab$, where $a, b \in I$.

Understanding the localization of a module

Computing projective dimension over hereditary rings (modules).

Graded Rings , divided polynomial algebra

Why is the boolean "OR" operator denoted as "+"?

A problem regarding a maximal ideal in a polynomial ring in several variables

$\mathbb Z [x]$ module structure on $\mathbb Z$

Prove: $R$ is local $\iff$ $R$ has exactly one maximal ideal.

$R$ be local and suppose $x ∈ R$ satisfies $x^2 = x$

Prove that $x−1$ and $y−1$ are irreducible in $R$

Show $2$ is not prime in $\{f\in\mathbb{Q}[x]:f(m)\in\mathbb{Z}\text{ for all }m\in\mathbb{N}\}$

Arithmetic of quotients

For which $n$ is $\sum_{i=0}^n x^i\in\mathbb{Q}[x]$ irreducible?

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