List questions from ring-theory

Published on 25 Mar 2026 - 6:04

105

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Pre-image of element in quaternion algebra

Published on 26 Mar 2026 - 1:22

59

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Applying degree 2 or 3 irreducibility tests to higher degree

Published on 25 Mar 2026 - 12:15

45

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Reducing an approximation claim from a prime ideal to a maximal ideal

Published on 15 Feb 2019 - 14:07

104

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Show that $\Bbb Z[\alpha,4/\alpha]/(2)$ is a direct product of three domains, where $\alpha^3+\alpha^2-2\alpha+8=0$

Published on 30 Mar 2026 - 11:37

168

Views

${(F^*)}^{-1}(m)$ is maximal ideal where $m$ is maximal

Published on 26 Mar 2026 - 1:06

145

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Left Adjoint to the Forgetful Functor from Rings to Semirings.

Published on 25 Mar 2026 - 6:12

136

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Show that $n^2-1+n \sqrt{d}$ is always a unit in $\mathbb{Z}[\sqrt{d}]$

Published on 16 Feb 2019 - 17:26

646

Views

Show that $n^2-1+n\sqrt{d}$ is the fundamental unit in $\mathbb{Z}[\sqrt{d}]$ for all $n\geq 3$

Published on 16 Feb 2019 - 19:02

64

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Why is $k[x_1] \to A$ not finite and $\phi(y)=x_1+x_2$ finite?

Published on 01 Apr 2026 - 11:59

126

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The set of one-sided inverses is not a group under multiplication

Published on 17 Feb 2019 - 16:14

149

Views

Proving the surjective property in Chinese Remainder Theorem

Published on 25 Mar 2026 - 15:47

1.4k

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Ideal generated by two elements is maximal in $\mathbb{Z}[x]$

Published on 29 Mar 2026 - 4:48

764

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Proving that sum of two elements is not invertible in a ring

Published on 17 Feb 2019 - 21:11

85

Views

Ideal of $\mathbb{Z}[x]$ generated by $3$ and $x^2+1$ is proper

Published on 30 Mar 2026 - 11:37

List Question

Integral domain which contains a copy of its fraction field

Pre-image of element in quaternion algebra

Applying degree 2 or 3 irreducibility tests to higher degree

Reducing an approximation claim from a prime ideal to a maximal ideal

Show that $\Bbb Z[\alpha,4/\alpha]/(2)$ is a direct product of three domains, where $\alpha^3+\alpha^2-2\alpha+8=0$

${(F^*)}^{-1}(m)$ is maximal ideal where $m$ is maximal

Left Adjoint to the Forgetful Functor from Rings to Semirings.

Show that $n^2-1+n \sqrt{d}$ is always a unit in $\mathbb{Z}[\sqrt{d}]$

Show that $n^2-1+n\sqrt{d}$ is the fundamental unit in $\mathbb{Z}[\sqrt{d}]$ for all $n\geq 3$

Why is $k[x_1] \to A$ not finite and $\phi(y)=x_1+x_2$ finite?

The set of one-sided inverses is not a group under multiplication

Proving the surjective property in Chinese Remainder Theorem

Ideal generated by two elements is maximal in $\mathbb{Z}[x]$

Proving that sum of two elements is not invertible in a ring

Ideal of $\mathbb{Z}[x]$ generated by $3$ and $x^2+1$ is proper

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