List questions from ring-theory

Published on 25 Mar 2026 - 17:45

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I want to know how to prove ideal

Published on 29 Mar 2026 - 23:25

114

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When $\langle f(x),y \rangle$ is a radical ideal?

Published on 29 Mar 2026 - 23:24

72

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$R=\{f(x)\in \mathbb{Q}[x] | f'(0)=0 \}$ is not PID

Published on 27 Mar 2026 - 15:15

166

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If $a^2=a$ find the inverse of $1+a$

Published on 25 Mar 2026 - 17:19

483

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Why $f(x) = 5x$ is not a ring homomorphism?

Published on 25 Mar 2026 - 6:11

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What is an irreducible element in $\Bbb{Z}_6[x]$?

Published on 28 Mar 2026 - 20:58

743

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If $R$ is a principal ideal domain and $s$ is a non-zero prime ideal, then $\frac{R}{s}$ has finitely many prime ideals .

Published on 27 Mar 2026 - 15:10

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$x^{2n} + x^{2n-1} + x^ {2n-2} +\ldots+ x + 1$ is irreducible for any $n\in \mathbb N$ in $F_2[x]$. True or false?

Published on 26 Mar 2026 - 7:35

322

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Isomorphisms for rings modulo ideals

Published on 25 Mar 2026 - 20:34

60

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Is it true that he polynomial $\frac{x^p- 1}{x-1}$ ($p$ is prime) is irreducible in $\mathbb{F}_2[x]$ iff $p$ is prime?

Published on 26 Mar 2026 - 7:35

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When is the localization map injective?

Published on 26 Mar 2026 - 0:58

80

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Quotient $\mathbf{F}_3[X]/(X^5+1)$

Published on 26 Mar 2026 - 7:33

2.8k

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Flaw of proof: polynomial ring is integrally closed if the coefficient ring is integrally closed

Published on 15 Dec 2018 - 6:05

316

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If $ab - ba = c, bc - cb = a, ca - ac = b$ in a ring, prove that $a^2 + b^2 + c^2$ commutes with $a, b$ and $c$.

Published on 25 Mar 2026 - 12:27

List Question

Coordinate ring of a scheme in functorial algebraic geometry

I want to know how to prove ideal

When $\langle f(x),y \rangle$ is a radical ideal?

$R=\{f(x)\in \mathbb{Q}[x] | f'(0)=0 \}$ is not PID

If $a^2=a$ find the inverse of $1+a$

Why $f(x) = 5x$ is not a ring homomorphism?

What is an irreducible element in $\Bbb{Z}_6[x]$?

If $R$ is a principal ideal domain and $s$ is a non-zero prime ideal, then $\frac{R}{s}$ has finitely many prime ideals .

$x^{2n} + x^{2n-1} + x^ {2n-2} +\ldots+ x + 1$ is irreducible for any $n\in \mathbb N$ in $F_2[x]$. True or false?

Isomorphisms for rings modulo ideals

Is it true that he polynomial $\frac{x^p- 1}{x-1}$ ($p$ is prime) is irreducible in $\mathbb{F}_2[x]$ iff $p$ is prime?

When is the localization map injective?

Quotient $\mathbf{F}_3[X]/(X^5+1)$

Flaw of proof: polynomial ring is integrally closed if the coefficient ring is integrally closed

If $ab - ba = c, bc - cb = a, ca - ac = b$ in a ring, prove that $a^2 + b^2 + c^2$ commutes with $a, b$ and $c$.

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