List questions from polynomial-rings

Published on 09 May 2021 - 1:09

39

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Finding the inverse of $(x^2+2)$ in the field $S = \Bbb F_3[x]/(x^4+x^3+x^2+1)$

Published on 10 May 2021 - 22:00

40

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Why a field $F$ sits naturally inside the ring $F[x]_{m(x)}$ for $m(x)\in F[x]$?

Published on 23 May 2021 - 7:23

109

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Prove that $\mathbb{F}_2[X] / \left(x^3 + x + 1 \right)$ is a field with 8 elements

Published on 25 May 2021 - 15:50

58

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Is $\mathbb{C}[X, Y] / (X^5 + Y - 13)$ integrally closed?

Published on 27 Mar 2026 - 8:41

56

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Show that $R[x]/\langle P \rangle$ is a free R-Module and R-Algebra

Published on 08 Jun 2021 - 15:22

57

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How do I go between generators and elements of an ideal in $_2[x_1,...,x_n]$?

Published on 25 Mar 2026 - 8:00

117

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Factorizations and roots of a bivariate polynomial

Published on 29 Jun 2021 - 21:51

73

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Simplifying a tensor product

Published on 09 Jul 2021 - 21:58

61

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Proof that $(v_n)=(1+t)^n$ is a basis for $K[t]$

Published on 22 Aug 2021 - 9:57

105

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Showing $k[X] \cong k[X,Y,Z]\big/{(Y-X^2,Z-X^3)}$

Published on 01 Sep 2021 - 12:51

99

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Kernel of the polynomial to function map?

Published on 04 Sep 2021 - 19:32

258

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Let $g(x),h(x)\in\mathbb{Z}[x]$ and $h(x)$ is monic. If $h(x)$ divides $g(x)$ in $\mathbb{Q}[x]$ then $h(x)$ divides $g(x)$ in $\mathbb{Z}[x]$

Published on 13 Sep 2021 - 15:29

181

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"Mod" out symmetry in ideal for a Groebner basis calculation (using a quotient ring?)

Published on 29 Mar 2026 - 1:35

134

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Sutructure of the ideal of vanishing polynomials on $\mathbb{F}_p$

Published on 05 Oct 2021 - 20:50

List Question

Prove: If $f,g \in \Bbb Z[x]$ then $C(fg) = C(f)C(g)$

Finding the inverse of $(x^2+2)$ in the field $S = \Bbb F_3[x]/(x^4+x^3+x^2+1)$

Why a field $F$ sits naturally inside the ring $F[x]_{m(x)}$ for $m(x)\in F[x]$?

Prove that $\mathbb{F}_2[X] / \left(x^3 + x + 1 \right)$ is a field with 8 elements

Is $\mathbb{C}[X, Y] / (X^5 + Y - 13)$ integrally closed?

Show that $R[x]/\langle P \rangle$ is a free R-Module and R-Algebra

How do I go between generators and elements of an ideal in $_2[x_1,...,x_n]$?

Factorizations and roots of a bivariate polynomial

Simplifying a tensor product

Proof that $(v_n)=(1+t)^n$ is a basis for $K[t]$

Showing $k[X] \cong k[X,Y,Z]\big/{(Y-X^2,Z-X^3)}$

Kernel of the polynomial to function map?

Let $g(x),h(x)\in\mathbb{Z}[x]$ and $h(x)$ is monic. If $h(x)$ divides $g(x)$ in $\mathbb{Q}[x]$ then $h(x)$ divides $g(x)$ in $\mathbb{Z}[x]$

"Mod" out symmetry in ideal for a Groebner basis calculation (using a quotient ring?)

Sutructure of the ideal of vanishing polynomials on $\mathbb{F}_p$

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