List questions from ring-theory

Published on 15 Apr 2026 - 8:27

333

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For an integral domain $D$, $na = 0$ where $n \in \mathbb{Z}, n\neq 0$ for some $a \in D - \{0\}$, then $D$ is of finite characteristic.

Published on 11 Apr 2026 - 23:25

38

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Problem about kernels as ideals and the First Isomorphism Theorem

Published on 26 Mar 2026 - 7:57

182

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Showing that an element generates the kernel of a homomorphism

Published on 13 Apr 2026 - 3:46

99

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$M$ maximal iff $\bar{M}$ is maximal

Published on 15 Apr 2026 - 18:28

41

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Prove that radical of an ideal is contained in the Jacobson of the ideal

Published on 13 Apr 2026 - 16:01

40

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Why $R[x,y,z,・・・] /（x^2,y^2,z^2,・・・）$ is $0$ dimmensional?

Published on 11 May 2026 - 7:22

98

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Why is the ideal $\langle x^2, 2\rangle$ of $\mathbb{Z}[x]$ a primary ideal?

Published on 14 Apr 2026 - 3:21

48

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Confusion with integral domains

Published on 12 Apr 2026 - 15:30

77

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Find all ring maps $\mathbb{Q}[x]/(x^{101}+2)\longrightarrow\mathbb{Q}[x]/(x^{501}-2)$

Published on 17 Apr 2026 - 0:39

382

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Left ideals of the ring $M_2(\Bbb Z_2)$

Published on 16 Apr 2026 - 21:45

93

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Given a nonconstant $f\in \Bbb C[x]$, condition for every finitely generated indecomposable $\Bbb C[x]/(f)$-module is projective

Published on 13 Apr 2026 - 5:28

343

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Is the number of orderings the same of the number of automorphisms in a ring?

Published on 09 Apr 2026 - 12:03

412

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Isn't $I$ a maximal ideal in $\Bbb Z_{11} [X]$?

Published on 11 Apr 2026 - 17:55

173

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In what rings is every ideal a fractional ideal?

Published on 10 Apr 2026 - 1:15

List Question

Characterization of invertible elements of a ring

For an integral domain $D$, $na = 0$ where $n \in \mathbb{Z}, n\neq 0$ for some $a \in D - \{0\}$, then $D$ is of finite characteristic.

Problem about kernels as ideals and the First Isomorphism Theorem

Showing that an element generates the kernel of a homomorphism

$M$ maximal iff $\bar{M}$ is maximal

Prove that radical of an ideal is contained in the Jacobson of the ideal

Why $R[x,y,z,・・・] /（x^2,y^2,z^2,・・・）$ is $0$ dimmensional?

Why is the ideal $\langle x^2, 2\rangle$ of $\mathbb{Z}[x]$ a primary ideal?

Confusion with integral domains

Find all ring maps $\mathbb{Q}[x]/(x^{101}+2)\longrightarrow\mathbb{Q}[x]/(x^{501}-2)$

Left ideals of the ring $M_2(\Bbb Z_2)$

Given a nonconstant $f\in \Bbb C[x]$, condition for every finitely generated indecomposable $\Bbb C[x]/(f)$-module is projective

Is the number of orderings the same of the number of automorphisms in a ring?

Isn't $I$ a maximal ideal in $\Bbb Z_{11} [X]$?

In what rings is every ideal a fractional ideal?

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