List questions from unique-factorization-domains

Published on 15 Apr 2026 - 7:13

43

Views

How can I find irreducible polynomials in $Z_{77}[x]$?

Published on 14 Apr 2026 - 2:53

75

Views

How to show that some elements of $\mathbb{Z}[2\sqrt{2}]$ are irreducible?

Published on 12 Apr 2026 - 4:04

244

Views

Nonzero prime ideal containing no other nonzero prime ideal

Published on 16 Apr 2026 - 10:26

113

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Uniqueness of solutions in complex linear equations.

Published on 12 Apr 2026 - 7:43

273

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Inverse of a finitely generated ideal in UFD

Published on 12 Apr 2026 - 2:53

609

Views

How to prove that $k[x,x^{-1},y]$ is a UFD

Published on 13 Apr 2026 - 11:28

94

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GCD in unique factorization domain

Published on 13 Apr 2026 - 2:37

107

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Factorization in $\mathbb{Z}[x]$?

Published on 08 Apr 2026 - 18:06

117

Views

Surjective Map between UFD and PID

Published on 14 Apr 2026 - 14:24

33

Views

Let $F=2X^3-X^2+5X-6$, $G \in \mathbb{R}[X]$, $\deg(G)=2$. If $F + G$ has roots $-1,0,1$, find lowest degree $H$ s.t. $G\mid H$, $\gcd(H,H')=X^2(X-6)$

Published on 16 Apr 2026 - 10:08

42

Views

Finding minimal polynomials $f \in \mathbb{Z}[x]$ with additional restrictions

Published on 12 Apr 2026 - 3:28

35

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Find every $a,b \in \mathbb{C}$ such that dividing $P=3X^{120}+\sqrt{2}X^{19}+aX^{11}+\sqrt{2}X^9+3X^2+b$ by $Q=X^2+1$ has remainder $R=5X+2$

Published on 17 Apr 2026 - 12:25

221

Views

How to show if $(f)=(c)(g)$ where $c \in R$ (UFD) and $g$ is primitive , then $(c)=(\mathrm{cont}_f)$ where $\mathrm{cont}_f$ is the content of $f$.

Published on 14 Apr 2026 - 20:49

612

Views

On quotient of UFD

Published on 13 Apr 2026 - 18:00

List Question

A property of unique factorization domains

How can I find irreducible polynomials in $Z_{77}[x]$?

How to show that some elements of $\mathbb{Z}[2\sqrt{2}]$ are irreducible?

Nonzero prime ideal containing no other nonzero prime ideal

Uniqueness of solutions in complex linear equations.

Inverse of a finitely generated ideal in UFD

How to prove that $k[x,x^{-1},y]$ is a UFD

GCD in unique factorization domain

Factorization in $\mathbb{Z}[x]$?

Surjective Map between UFD and PID

Let $F=2X^3-X^2+5X-6$, $G \in \mathbb{R}[X]$, $\deg(G)=2$. If $F + G$ has roots $-1,0,1$, find lowest degree $H$ s.t. $G\mid H$, $\gcd(H,H')=X^2(X-6)$

Finding minimal polynomials $f \in \mathbb{Z}[x]$ with additional restrictions

Find every $a,b \in \mathbb{C}$ such that dividing $P=3X^{120}+\sqrt{2}X^{19}+aX^{11}+\sqrt{2}X^9+3X^2+b$ by $Q=X^2+1$ has remainder $R=5X+2$

How to show if $(f)=(c)(g)$ where $c \in R$ (UFD) and $g$ is primitive , then $(c)=(\mathrm{cont}_f)$ where $\mathrm{cont}_f$ is the content of $f$.

On quotient of UFD

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