List questions from ring-theory

Published on 16 Apr 2026 - 0:03

130

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Prove that $\mathbb{Z}[i]/(3)$ and $\mathbb{Z}[i]/(7)$ are finite fields and find their cardinality

Published on 13 Apr 2026 - 22:24

109

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Are the ring $\mathbb{R}[x]/(x^{2})$ and $\mathbb{R}[x]/(x^{3})$ isomorphic?

Published on 26 Mar 2026 - 7:58

38

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Is it true that $b(R/(a))=((a)+(b))/(a)$ as quotient ring

Published on 16 Apr 2026 - 11:05

35

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Grillet, Proposition VI.9.2 (minor detail)

Published on 10 May 2026 - 14:30

108

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Certificate of unsatisfiability for system of equations over a ring

Published on 15 Apr 2026 - 6:27

76

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Prove non-constant, irreducible polynomials are primitive

Published on 15 Apr 2026 - 1:34

75

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Generalisation of $\text{ker}f \bigoplus \text{Im}f \cong M$

Published on 16 Apr 2026 - 12:27

39

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Is it possible to introduce infinitely large quantities without introducing infinitesimals?

Published on 28 Mar 2026 - 20:55

334

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Find a necessary and sufficient condition for $U(m)$ and $U(n)$ to be isomorphic.

Published on 16 Apr 2026 - 2:28

63

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How to classify the quotients of $\mathbb{Z}_p[X]$

Published on 10 Apr 2026 - 17:24

343

Views

$R^\mathbb{N}$ is not finitely generated as an $R$-module

Published on 12 Apr 2026 - 21:35

253

Views

Commutative ring instead of field: proof that the group of $n\times n$ unitriangular matrices is solvable

Published on 29 Apr 2026 - 14:17

952

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Formal power series are a euclidean ring

Published on 26 Mar 2026 - 6:34

87

Views

Which notation is best for $R/I$

Published on 26 Mar 2026 - 14:17

List Question

Show that $x^3 + 3x+2$ is irreducible in $\mathbb{Z}[5]$

Prove that $\mathbb{Z}[i]/(3)$ and $\mathbb{Z}[i]/(7)$ are finite fields and find their cardinality

Are the ring $\mathbb{R}[x]/(x^{2})$ and $\mathbb{R}[x]/(x^{3})$ isomorphic?

Is it true that $b(R/(a))=((a)+(b))/(a)$ as quotient ring

Grillet, Proposition VI.9.2 (minor detail)

Certificate of unsatisfiability for system of equations over a ring

Prove non-constant, irreducible polynomials are primitive

Generalisation of $\text{ker}f \bigoplus \text{Im}f \cong M$

Is it possible to introduce infinitely large quantities without introducing infinitesimals?

Find a necessary and sufficient condition for $U(m)$ and $U(n)$ to be isomorphic.

How to classify the quotients of $\mathbb{Z}_p[X]$

$R^\mathbb{N}$ is not finitely generated as an $R$-module

Commutative ring instead of field: proof that the group of $n\times n$ unitriangular matrices is solvable

Formal power series are a euclidean ring

Which notation is best for $R/I$

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