List questions from polynomial-rings

Published on 09 Apr 2026 - 8:49

98

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Show the following polynomial is Irreducible over the given ring

Published on 15 Apr 2026 - 10:58

241

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What does it mean by that $E$ is a finite extension of $F$, when $F\subseteq E$ is not clear?

Published on 14 Apr 2026 - 12:20

296

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Please help me understand "The Weak Nullstellensatz."

Published on 14 Apr 2026 - 14:22

530

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Is there an efficient algorithm to find all zeros of systems of multivariate polynomial equations over a finite field?

Published on 10 May 2026 - 19:03

48

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Defining an evaluation map between $\mathbb{Q}\lbrack x \rbrack$ and $\mathbb{Q}\lbrack x \rbrack/(x^2-5)$

Published on 19 Apr 2026 - 4:15

475

Views

coprime ideals in $K[X]$

Published on 14 Apr 2026 - 14:04

204

Views

GCDs for the polynomial ring over a Galois field.

Published on 10 May 2026 - 20:02

108

Views

Find all of homomorphisms $Φ$ from $\mathbb C$[$x$]/$I$ to $\mathbb C$ that satisfies specific condition

Published on 16 Apr 2026 - 9:54

61

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Applying degree 2 or 3 irreducibility tests to higher degree

Published on 15 Apr 2026 - 4:13

239

Views

Showing if $R$ is a PID and $0\neq r\in R$ is irreducible, then $R[X]/(r)\cong (R/(r))[X]$

Published on 14 Apr 2026 - 19:19

134

Views

Does there always exist a linear shift of a given polynomial such that all coefficients are nonzero?

Published on 11 Apr 2026 - 19:08

498

Views

Subring of polynomial ring containing two polynomials of relatively prime degree

Published on 15 Apr 2026 - 19:46

268

Views

Product of ideals in $\mathbb{Z}[X]$

Published on 09 Apr 2026 - 21:35

240

Views

Prime ideals in $\mathbb{Z}[X], \mathbb{Q}[X], \mathbb{F}_{19}[X]$.

Published on 10 May 2026 - 17:13

List Question

Counterexample PID

Show the following polynomial is Irreducible over the given ring

What does it mean by that $E$ is a finite extension of $F$, when $F\subseteq E$ is not clear?

Please help me understand "The Weak Nullstellensatz."

Is there an efficient algorithm to find all zeros of systems of multivariate polynomial equations over a finite field?

Defining an evaluation map between $\mathbb{Q}\lbrack x \rbrack$ and $\mathbb{Q}\lbrack x \rbrack/(x^2-5)$

coprime ideals in $K[X]$

GCDs for the polynomial ring over a Galois field.

Find all of homomorphisms $Φ$ from $\mathbb C$[$x$]/$I$ to $\mathbb C$ that satisfies specific condition

Applying degree 2 or 3 irreducibility tests to higher degree

Showing if $R$ is a PID and $0\neq r\in R$ is irreducible, then $R[X]/(r)\cong (R/(r))[X]$

Does there always exist a linear shift of a given polynomial such that all coefficients are nonzero?

Subring of polynomial ring containing two polynomials of relatively prime degree

Product of ideals in $\mathbb{Z}[X]$

Prime ideals in $\mathbb{Z}[X], \mathbb{Q}[X], \mathbb{F}_{19}[X]$.

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