List questions from ring-theory

Published on 13 Apr 2026 - 6:11

107

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A module $M$ is semiartinian if and only if $M$ is artinian. when $M$ is noetherian.

Published on 15 Apr 2026 - 7:13

214

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Symmetric tensor polynomials generated by power sums?

Published on 14 Apr 2026 - 20:18

398

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When do the units of a ring together with 0 form a field?

Published on 28 Apr 2026 - 8:34

276

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Subrings of $\Bbb Z_p$

Published on 14 Apr 2026 - 3:38

113

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Minimality of the Generator of a Kernel

Published on 11 Apr 2026 - 6:46

87

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Example of ring such that for an element $s \in R$, the set $sR$ does not contain $s$

Published on 12 Apr 2026 - 16:46

108

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If A has characteristic 3, and 5a = 0, then a = 0.

Published on 16 Apr 2026 - 13:58

32

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What does $S[\lambda_1,...,\lambda_n]$ look like? Where $S$ is a subring of a given ring $R$ and $\lambda_1,\ldots,\lambda_n\in R$.

Published on 15 Apr 2026 - 16:40

292

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Dummit and Foote's proof that $(\mathbb{Z}/p^{\alpha}\mathbb{Z})^*$ is cyclic of order $p^{\alpha - 1}(p-1)$

Published on 16 Apr 2026 - 10:23

361

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Frobenius automorphism for primes ramified over field extension

Published on 12 Apr 2026 - 23:54

41

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How should one interpret $R[A_1,..,A_n]$ where $R$ is a unital ring and $A_i\in M_{n\times n}(R)$

Published on 14 Apr 2026 - 11:33

43

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Prove that set of all non principal ideals of an integral domain has a maximal element

Published on 13 Apr 2026 - 17:24

347

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Can a Unique Factorisation Domain be non-commutative?

Published on 11 May 2026 - 7:16

29

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Annihilators of a module.

Published on 12 Apr 2026 - 10:38

List Question

The elements in a principal ideal

A module $M$ is semiartinian if and only if $M$ is artinian. when $M$ is noetherian.

Symmetric tensor polynomials generated by power sums?

When do the units of a ring together with 0 form a field?

Subrings of $\Bbb Z_p$

Minimality of the Generator of a Kernel

Example of ring such that for an element $s \in R$, the set $sR$ does not contain $s$

If A has characteristic 3, and 5a = 0, then a = 0.

What does $S[\lambda_1,...,\lambda_n]$ look like? Where $S$ is a subring of a given ring $R$ and $\lambda_1,\ldots,\lambda_n\in R$.

Dummit and Foote's proof that $(\mathbb{Z}/p^{\alpha}\mathbb{Z})^*$ is cyclic of order $p^{\alpha - 1}(p-1)$

Frobenius automorphism for primes ramified over field extension

How should one interpret $R[A_1,..,A_n]$ where $R$ is a unital ring and $A_i\in M_{n\times n}(R)$

Prove that set of all non principal ideals of an integral domain has a maximal element

Can a Unique Factorisation Domain be non-commutative?

Annihilators of a module.

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