List questions from ring-theory

Published on 25 Mar 2026 - 8:30

142

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Find the inverse of $5+4\sqrt[3]{2}+3\sqrt[3]{4}$?

Published on 25 Mar 2026 - 11:14

1.1k

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Let $F$ be a field. Show that if $p(x)$ is divided by $x-a$, the remainder is $p(a)$.

Published on 08 Apr 2018 - 20:02

2.6k

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If $F$ is a field, show that $F[x]$ is never a field.

Published on 08 Apr 2018 - 20:17

275

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Show that the ring isomorphism $\phi :R[x]\to S[x]$ is well-defined.

Published on 25 Mar 2026 - 23:40

56

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Determining irreducible elements and finding ideals

Published on 25 Mar 2026 - 21:30

168

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Continuous map from $\text{Spec}(R/I)$ to $\text{Spec}(R)$ induced by the canonical projection homomorphism

Published on 25 Mar 2026 - 21:22

77

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Sum of two minimal direct summands

Published on 25 Mar 2026 - 4:39

61

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How to construction a division ring from the given field?

Published on 22 Mar 2026 - 16:27

522

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Question about a proof of $\mathbb{Z}[i]/(2+i)\cong \mathbb{Z}/5\mathbb{Z}$

Published on 19 Mar 2026 - 18:20

50

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Question about isomorphisms between $R[X]$ and $R \times R$

Published on 09 Apr 2018 - 21:05

73

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Dividing polynomials in $\mathbb{F}_7[x]$

Published on 09 Apr 2018 - 22:37

228

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In $Z_5[x]$ , find all monic divisors of degree two for $2x^2+4x^3+3x^3+2x+4$

Published on 25 Mar 2026 - 4:59

85

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$ R \cong R s $ as rings if and only if $ s $ is invertible

Published on 26 Mar 2026 - 1:31

3.5k

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Characteristic of infinite integral domain.

Published on 10 Apr 2018 - 7:15

List Question

Term for elements of a monoid in a corresponding monid ring

Find the inverse of $5+4\sqrt[3]{2}+3\sqrt[3]{4}$?

Let $F$ be a field. Show that if $p(x)$ is divided by $x-a$, the remainder is $p(a)$.

If $F$ is a field, show that $F[x]$ is never a field.

Show that the ring isomorphism $\phi :R[x]\to S[x]$ is well-defined.

Determining irreducible elements and finding ideals

Continuous map from $\text{Spec}(R/I)$ to $\text{Spec}(R)$ induced by the canonical projection homomorphism

Sum of two minimal direct summands

How to construction a division ring from the given field?

Question about a proof of $\mathbb{Z}[i]/(2+i)\cong \mathbb{Z}/5\mathbb{Z}$

Question about isomorphisms between $R[X]$ and $R \times R$

Dividing polynomials in $\mathbb{F}_7[x]$

In $Z_5[x]$ , find all monic divisors of degree two for $2x^2+4x^3+3x^3+2x+4$

$ R \cong R s $ as rings if and only if $ s $ is invertible

Characteristic of infinite integral domain.

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