List questions from polynomial-rings

Published on 03 Sep 2017 - 5:13

119

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Polynomial ring $\mathbb{Z}[X]/(X^{2^k} + 1)$ has property $X^{2^k} = −1$?

Published on 27 Mar 2026 - 12:20

208

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Problem related to the polynomial ring of several variables.

Published on 11 Sep 2017 - 2:46

671

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Ideal of a Polynomial ring $R$ which is not principal.

Published on 12 Sep 2017 - 1:26

202

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$r$ is a root of $f(X)$ if and only if $f(X)\in(X − r)$

Published on 17 Sep 2017 - 17:24

524

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Trying to prove that $\langle y-x^2, z-x^3\rangle$ is prime in $K[x,y,z]$

Published on 22 Sep 2017 - 10:25

62

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Show the following in the ring of polynomials in $x$, $y$ and $z$ with coefficients in $F$.

Published on 02 Oct 2017 - 12:58

289

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Is $k[x,y,z]/(y^2-xz)$ a UFD?

Published on 04 Oct 2017 - 21:50

1.8k

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Determining whether $(x^2-3)$ is a maximal ideal in $\mathbb{Z}[X]$

Published on 12 Oct 2017 - 8:53

58

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Can $\mathbb{R}[[X]]$ as the ring of one-sided sequences be extended to a field of two-sided sequences with termwise addition?

Published on 27 Mar 2026 - 16:09

32

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How to show each element of $\frac{Q[x]}{I}$ is of the form $a_0+a_1t+a_2t^2$

Published on 13 Oct 2017 - 20:43

1.5k

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Understanding Ideals and Quotients in Polynomial Rings of Multiple Variables

Published on 17 Oct 2017 - 2:51

47

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Showing $(q(X),q'(X)) = F[X]$

Published on 23 Oct 2017 - 15:03

128

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Polynomial differentiation map

Published on 30 Oct 2017 - 21:48

130

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Describing a $\mathbb{Z}$-algebra and its tensor with $\mathbb{Z}/2\mathbb{Z}$

Published on 04 Nov 2017 - 10:19

List Question

Polynomial rings over a commutative ring with identity

Polynomial ring $\mathbb{Z}[X]/(X^{2^k} + 1)$ has property $X^{2^k} = −1$?

Problem related to the polynomial ring of several variables.

Ideal of a Polynomial ring $R$ which is not principal.

$r$ is a root of $f(X)$ if and only if $f(X)\in(X − r)$

Trying to prove that $\langle y-x^2, z-x^3\rangle$ is prime in $K[x,y,z]$

Show the following in the ring of polynomials in $x$, $y$ and $z$ with coefficients in $F$.

Is $k[x,y,z]/(y^2-xz)$ a UFD?

Determining whether $(x^2-3)$ is a maximal ideal in $\mathbb{Z}[X]$

Can $\mathbb{R}[[X]]$ as the ring of one-sided sequences be extended to a field of two-sided sequences with termwise addition?

How to show each element of $\frac{Q[x]}{I}$ is of the form $a_0+a_1t+a_2t^2$

Understanding Ideals and Quotients in Polynomial Rings of Multiple Variables

Showing $(q(X),q'(X)) = F[X]$

Polynomial differentiation map

Describing a $\mathbb{Z}$-algebra and its tensor with $\mathbb{Z}/2\mathbb{Z}$

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