List questions from polynomial-rings

Published on 02 Jan 2022 - 14:11

157

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Show that $(x^3+x+1)$ is prime in $\mathbb{Z}/(2)[x]$

Published on 09 Jan 2022 - 10:56

466

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$\mathbb{C}[x,y,z]/(x^2+y^2+z^2-1)$ is not a UFD

Published on 17 Jan 2022 - 10:59

71

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$\phi: \mathbb{R}[X] \to \mathbb{C}$ is a homomorphism such that: $\phi(X) = 1 + i$. What is $\ker \phi$?

Published on 27 Mar 2026 - 15:07

164

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Ideal of Polynomial Function on a Circle that Vanish at a Point

Published on 19 Jan 2022 - 22:27

36

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Find $z \in \mathbb{Z}_3[x]$ such that $\alpha [z]_f=[x^2]_f$

Published on 01 Feb 2022 - 19:04

48

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Find a inverse of polynomial in quotient ring in $\mathbb{Z}_p$

Published on 07 Feb 2022 - 16:11

139

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Proving the induced function of the sum of two polynomials is the sum of the two induced functions

Published on 18 Feb 2022 - 23:56

137

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Finding isomorphism between galois field $ {\rm GF}(2^8)$ and polynomial ring of galois field ${\rm GF}(2^4)[X] / F[X]$

Published on 21 Feb 2022 - 6:19

51

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Do the following ideals generate the polynomial ring $K[x,y,z]$?

Published on 12 Mar 2022 - 13:43

60

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mod $p$ irreducibility test over $\mathbb{Z}$

Published on 17 Mar 2022 - 17:37

81

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A question about the proof $\dim(k[x_1,\dots,x_n]) = n$

Published on 28 Mar 2022 - 0:26

66

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Ring isomorphism between $(k[x,y]/(xy))/(x+y-a)$ and $k\times k$

Published on 27 Mar 2026 - 14:02

72

Views

$K[t^2,t^3]_{(t^2,t^3)}$ is not regular

Published on 25 Mar 2026 - 11:01

445

Views

Finite free resolution of a finitely generated $\mathbb Z[x_1,\ldots,x_n]$-module

Published on 28 Mar 2026 - 10:02

List Question

Determining if two ideals in $\mathbb{Q}[X,Y]$ are equal

Show that $(x^3+x+1)$ is prime in $\mathbb{Z}/(2)[x]$

$\mathbb{C}[x,y,z]/(x^2+y^2+z^2-1)$ is not a UFD

$\phi: \mathbb{R}[X] \to \mathbb{C}$ is a homomorphism such that: $\phi(X) = 1 + i$. What is $\ker \phi$?

Ideal of Polynomial Function on a Circle that Vanish at a Point

Find $z \in \mathbb{Z}_3[x]$ such that $\alpha [z]_f=[x^2]_f$

Find a inverse of polynomial in quotient ring in $\mathbb{Z}_p$

Proving the induced function of the sum of two polynomials is the sum of the two induced functions

Finding isomorphism between galois field $ {\rm GF}(2^8)$ and polynomial ring of galois field ${\rm GF}(2^4)[X] / F[X]$

Do the following ideals generate the polynomial ring $K[x,y,z]$?

mod $p$ irreducibility test over $\mathbb{Z}$

A question about the proof $\dim(k[x_1,\dots,x_n]) = n$

Ring isomorphism between $(k[x,y]/(xy))/(x+y-a)$ and $k\times k$

$K[t^2,t^3]_{(t^2,t^3)}$ is not regular

Finite free resolution of a finitely generated $\mathbb Z[x_1,\ldots,x_n]$-module

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