List questions from ring-theory

Published on 03 Feb 2018 - 18:42

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Localization of maximal ideal is again a maximal ideal and the residue fields are isomorphic

Published on 25 Mar 2026 - 6:05

132

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localizations and overrings of Dedekind domains with prescribed spectrum

Published on 22 Mar 2026 - 17:43

478

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If M is a a left module over $M_n(D)$ where $D$ is a division ring, M is Noetherian iff Artinian

Published on 22 Mar 2026 - 4:54

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Finite dimensional associative division algebras over Q

Published on 04 Feb 2018 - 10:01

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For which $n$ , does normal subgroups of $SL(2, \mathbb Z/n \mathbb Z)$ remain normal in $GL(2, \mathbb Z/n\mathbb Z)$?

Published on 25 Mar 2026 - 1:17

212

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$\Bbb{Z}[X]$ embeds in $\Bbb{Z}_2 \times \Bbb{Z}_3 \times \Bbb{Z}_5 \times \cdots$?

Published on 25 Mar 2026 - 4:58

2k

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Intersection of subrings

Published on 04 Feb 2018 - 18:42

72

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Clarification on Cayley-Hamilton theorem

Published on 23 Mar 2026 - 15:35

134

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A curious extension of real number field?

Published on 25 Mar 2026 - 3:07

254

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Artin's Proposition 11.5.5: Adjoining Elements

Published on 05 Feb 2018 - 2:47

168

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For coprime ideals $ I_1,\dots,I_n$ of $R$ and module $M$, we have $(I_1 I_2 \cdots I_n) M= I_1 M \cap \cdots\cap I_n M$

Published on 25 Mar 2026 - 10:24

105

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Taking quotients is left exact

Published on 05 Feb 2018 - 12:45

1.3k

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Ideal Generated by Nilpotent Elements is a Nilpotent Ideal

Published on 20 Mar 2026 - 3:00

93

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Distributive law over submodules

Published on 05 Feb 2018 - 19:15

List Question

$\mathbb Z[x]/(9x^2+1)$ has a prime ideal which is not maximal

Localization of maximal ideal is again a maximal ideal and the residue fields are isomorphic

localizations and overrings of Dedekind domains with prescribed spectrum

If M is a a left module over $M_n(D)$ where $D$ is a division ring, M is Noetherian iff Artinian

Finite dimensional associative division algebras over Q

For which $n$ , does normal subgroups of $SL(2, \mathbb Z/n \mathbb Z)$ remain normal in $GL(2, \mathbb Z/n\mathbb Z)$?

$\Bbb{Z}[X]$ embeds in $\Bbb{Z}_2 \times \Bbb{Z}_3 \times \Bbb{Z}_5 \times \cdots$?

Intersection of subrings

Clarification on Cayley-Hamilton theorem

A curious extension of real number field?

Artin's Proposition 11.5.5: Adjoining Elements

For coprime ideals $ I_1,\dots,I_n$ of $R$ and module $M$, we have $(I_1 I_2 \cdots I_n) M= I_1 M \cap \cdots\cap I_n M$

Taking quotients is left exact

Ideal Generated by Nilpotent Elements is a Nilpotent Ideal

Distributive law over submodules

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