List questions from unique-factorization-domains

Published on 09 Apr 2019 - 3:17

40

Views

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

Published on 14 Apr 2019 - 17:12

72

Views

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

Published on 23 Apr 2019 - 16:04

241

Views

Nonzero prime ideal containing no other nonzero prime ideal

Published on 01 Jun 2019 - 8:33

110

Views

Uniqueness of solutions in complex linear equations.

Published on 11 Jun 2019 - 16:52

270

Views

Inverse of a finitely generated ideal in UFD

Published on 17 Jun 2019 - 3:46

606

Views

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

Published on 19 Jun 2019 - 12:17

91

Views

GCD in unique factorization domain

Published on 23 Jun 2019 - 19:56

104

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

Published on 28 Jun 2019 - 0:22

114

Views

Surjective Map between UFD and PID

Published on 30 Jun 2019 - 14:13

30

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 01 Jul 2019 - 9:48

39

Views

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

Published on 02 Jul 2019 - 22:01

32

Views

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 02 Jul 2019 - 22:26

218

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 13 Jul 2019 - 18:56

608

Views

On quotient of UFD

Published on 31 Jul 2019 - 4:22

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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