List questions from ring-theory

Published on 13 Apr 2026 - 13:55

41

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Field extension coming from quotient maximal ideals

Published on 11 Apr 2026 - 4:04

47

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Confusion about proof of Nakayama's Lemma

Published on 10 Apr 2026 - 0:25

251

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characteristics of rings (2)

Published on 13 Apr 2026 - 10:42

432

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Prove, that $p\in\mathbb{R}[x]$ with $p=x^2+ax+b$ is irreducible if and only if $a^2<4b$.

Published on 15 Apr 2026 - 18:07

601

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An example of a field extension which is not Galois.

Published on 11 Apr 2026 - 8:37

332

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Unital ring $R$ such that $a^2=a$ for every $a\in R$

Published on 12 Apr 2026 - 21:21

273

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Krull dimension with Grobner bases

Published on 25 Mar 2026 - 12:20

589

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What is the characteristics polynomial of some element of the extended field over the base field?

Published on 16 Apr 2026 - 4:51

32

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Non-local ring $A$ with an ideal $I$ such that $1 + I \subseteq A^{*}$

Published on 05 May 2026 - 0:06

41

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Can we say that $m_{T_y} = m_y$?

Published on 24 Apr 2026 - 2:24

2.5k

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A ring $R$ has no nonzero nilpotent elements

Published on 14 Apr 2026 - 5:10

73

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In $\mathbb Z[x]$, find an ideal $P$ such that $R/P$ consists of $4$ elements.

Published on 13 Apr 2026 - 17:14

807

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Inverse element of $x^2 + x + 1$ in $\mathbb Z_2[x]/\langle x^3 + x + 1\rangle$

Published on 17 Apr 2026 - 10:58

418

Views

Show $\mathbb{Z}_{(p)} [ \sqrt{D}]$ is a UFD

Published on 04 May 2026 - 21:04

List Question

Determine all the prime ideals.

Field extension coming from quotient maximal ideals

Confusion about proof of Nakayama's Lemma

characteristics of rings (2)

Prove, that $p\in\mathbb{R}[x]$ with $p=x^2+ax+b$ is irreducible if and only if $a^2<4b$.

An example of a field extension which is not Galois.

Unital ring $R$ such that $a^2=a$ for every $a\in R$

Krull dimension with Grobner bases

What is the characteristics polynomial of some element of the extended field over the base field?

Non-local ring $A$ with an ideal $I$ such that $1 + I \subseteq A^{*}$

Can we say that $m_{T_y} = m_y$?

A ring $R$ has no nonzero nilpotent elements

In $\mathbb Z[x]$, find an ideal $P$ such that $R/P$ consists of $4$ elements.

Inverse element of $x^2 + x + 1$ in $\mathbb Z_2[x]/\langle x^3 + x + 1\rangle$

Show $\mathbb{Z}_{(p)} [ \sqrt{D}]$ is a UFD

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