List questions from ring-theory

Published on 21 May 2018 - 21:11

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Why does the smallest ring have two elements at least?

Published on 22 May 2018 - 7:18

268

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Determine all the ideals of $\mathbb{Q}[x,y]$ that contain the ideal $\langle x^2,y^2,xy\rangle$.

Published on 25 Mar 2026 - 4:42

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Definition of prime element in euclidean ring

Published on 22 May 2018 - 10:27

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Understanding the equivalence classes for $\Bbb R[x]/\langle x^2+1\rangle$

Published on 22 May 2018 - 13:56

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Why is the irreducibility of $x^3+3x+1 \in \mathbb{Q}[x]$ a consequence of its irreducibility in $\mathbb{F}_2[x]$?

Published on 23 May 2018 - 5:33

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Is $\{a+b\sqrt{3}\mid a, b \in \Bbb Z\}$ Ring?

Published on 23 May 2018 - 6:48

174

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$\Bbb F_p(\alpha)\cong\Bbb F_p[x]/(f(x))$

Published on 25 Mar 2026 - 9:53

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Check whether two given given rings are isomorphic

Published on 25 Mar 2026 - 16:07

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Proving $a+a =0$ for Boolean ring

Published on 23 May 2018 - 15:07

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Maximal ideal in Euclidean Ring

Published on 23 May 2018 - 21:05

51

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Multiple quotients of Ideals

Published on 27 Mar 2026 - 12:02

62

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A question on the product of integral homomorphisms

Published on 24 Mar 2026 - 23:45

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Let $B=\mathbb{R}[X,Y]$ and $I=(X^2-Y^3)$, show that in $A=B/I$, $\bar{X}$ is irreducible

Published on 28 Mar 2026 - 11:54

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Number of maximal ideals of a commutative ring with unity which is not a field.

Published on 25 Mar 2026 - 20:14

List Question

The prime element in Eisenstein ring

Why does the smallest ring have two elements at least?

Determine all the ideals of $\mathbb{Q}[x,y]$ that contain the ideal $\langle x^2,y^2,xy\rangle$.

Definition of prime element in euclidean ring

Understanding the equivalence classes for $\Bbb R[x]/\langle x^2+1\rangle$

Why is the irreducibility of $x^3+3x+1 \in \mathbb{Q}[x]$ a consequence of its irreducibility in $\mathbb{F}_2[x]$?

Is $\{a+b\sqrt{3}\mid a, b \in \Bbb Z\}$ Ring?

$\Bbb F_p(\alpha)\cong\Bbb F_p[x]/(f(x))$

Check whether two given given rings are isomorphic

Proving $a+a =0$ for Boolean ring

Maximal ideal in Euclidean Ring

Multiple quotients of Ideals

A question on the product of integral homomorphisms

Let $B=\mathbb{R}[X,Y]$ and $I=(X^2-Y^3)$, show that in $A=B/I$, $\bar{X}$ is irreducible

Number of maximal ideals of a commutative ring with unity which is not a field.

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