List questions from ring-theory

Published on 25 Mar 2026 - 14:30

348

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Prove that $R=\mathbb{Z}[i]$ is a Euclidean domain via $N(a+bi) = a^2+b^2. $

Published on 09 Nov 2019 - 20:46

37

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$\mathbb{K}[[x,y]]/\langle\, f\,\rangle \cong \mathbb{K}[[x]],\mathbb{K}[[y]]$. in formal power series ring

Published on 09 Nov 2019 - 22:48

77

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Prove that for each $f \in \mathbb{Q}[x]$ there exists $a+bx \in \mathbb{Q}[x]$ such that $f + \langle x^2 \rangle = (a+bx) + \langle x^2 \rangle$

Published on 17 Apr 2026 - 6:15

845

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Given a field $K$, the two ideals $(x^2 ,xy,y^2)$ and $(x,y)^2$ in $K[x,y]$ are the same.

Published on 16 Apr 2026 - 7:53

257

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${\rm Hom}_R(eR,eR)\cong eRe$ when $e$ is idempotent in ring $R$

Published on 16 Apr 2026 - 1:43

43

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Question about a quotient map of a ring

Published on 13 Apr 2026 - 21:43

82

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The ideals $(x^m,y^n)$ in $\Bbb Z[x,y]$ are $(x,y)$-primary

Published on 03 Apr 2026 - 11:56

57

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Ultimately show $R\cong S$ implies $R[x]\cong S[x]$.

Published on 09 Apr 2026 - 11:44

47

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Ring with power set, identity and neutral

Published on 12 Apr 2026 - 3:29

89

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Ring Homomorphism in field of rational functions of x and y with rational coefficients

Published on 22 Apr 2026 - 15:21

101

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Significance of unity in ring for isomorphism

Published on 22 Apr 2026 - 10:18

1.1k

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Prove that $R/I$ and $S/\phi(I)$ are isomorphic

Published on 03 Apr 2026 - 13:29

302

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Isomorphism between two matrix rings implies an isomorphism between two fields.

Published on 24 Apr 2026 - 9:38

540

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Endomorphism ring of a simple module

Published on 12 Apr 2026 - 0:04

List Question

Ring to field homomorphism

Prove that $R=\mathbb{Z}[i]$ is a Euclidean domain via $N(a+bi) = a^2+b^2. $

$\mathbb{K}[[x,y]]/\langle\, f\,\rangle \cong \mathbb{K}[[x]],\mathbb{K}[[y]]$. in formal power series ring

Prove that for each $f \in \mathbb{Q}[x]$ there exists $a+bx \in \mathbb{Q}[x]$ such that $f + \langle x^2 \rangle = (a+bx) + \langle x^2 \rangle$

Given a field $K$, the two ideals $(x^2 ,xy,y^2)$ and $(x,y)^2$ in $K[x,y]$ are the same.

${\rm Hom}_R(eR,eR)\cong eRe$ when $e$ is idempotent in ring $R$

Question about a quotient map of a ring

The ideals $(x^m,y^n)$ in $\Bbb Z[x,y]$ are $(x,y)$-primary

Ultimately show $R\cong S$ implies $R[x]\cong S[x]$.

Ring with power set, identity and neutral

Ring Homomorphism in field of rational functions of x and y with rational coefficients

Significance of unity in ring for isomorphism

Prove that $R/I$ and $S/\phi(I)$ are isomorphic

Isomorphism between two matrix rings implies an isomorphism between two fields.

Endomorphism ring of a simple module

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