List questions from polynomial-rings

Published on 18 Dec 2018 - 11:11

96

Views

Show the following polynomial is Irreducible over the given ring

Published on 21 Dec 2018 - 1:54

238

Views

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

Published on 31 Dec 2018 - 0:32

293

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Please help me understand "The Weak Nullstellensatz."

Published on 31 Dec 2018 - 9:41

529

Views

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

Published on 25 Mar 2026 - 4:40

45

Views

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

Published on 01 Feb 2019 - 2:10

471

Views

coprime ideals in $K[X]$

Published on 10 Feb 2019 - 4:19

201

Views

GCDs for the polynomial ring over a Galois field.

Published on 10 Feb 2019 - 21:40

105

Views

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

Published on 11 Feb 2019 - 23:45

58

Views

Applying degree 2 or 3 irreducibility tests to higher degree

Published on 14 Feb 2019 - 17:34

236

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 03 Mar 2019 - 1:43

131

Views

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

Published on 06 Mar 2019 - 20:32

495

Views

Subring of polynomial ring containing two polynomials of relatively prime degree

Published on 06 Mar 2019 - 22:53

266

Views

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

Published on 08 Mar 2019 - 23:55

237

Views

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

Published on 25 Mar 2026 - 7:43

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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