List questions from unique-factorization-domains

Published on 11 Apr 2026 - 2:07

113

Views

How to use norms to prove non-UFD?

Published on 11 Apr 2026 - 20:16

515

Views

If an element has prime norm in the ring of quadratic integers, then it is a prime element

Published on 15 Apr 2026 - 11:14

39

Views

What is different $(a_0, a_1, ..., a_d) = (1)$ and $\gcd(a_0, a_1, ..., a_d) = 1$ in arbitrary UFD?

Published on 15 Apr 2026 - 5:48

133

Views

Show for univariate relatively prime polynomials over a perfect field, that $\gcd(fg,(fg)')=\gcd(f,f')\gcd(g,g')$.

Published on 15 Apr 2026 - 23:55

463

Views

Find all discrete valuation subrings of $k(x)$

Published on 17 Apr 2026 - 2:53

127

Views

$f$ has a root in $F$ iff $f$ has a root in $\text{Frac}(F)$

Published on 17 Apr 2026 - 12:21

351

Views

Unique factorization of an element in an UFD

Published on 14 Apr 2026 - 0:32

384

Views

Is $\mathbb{Q}[x,y]/((x+y)^3-2)$ a UFD?

Published on 17 Apr 2026 - 6:56

531

Views

GCD expressed with irreducible elements in a unique factorization domain

Published on 14 Apr 2026 - 21:55

278

Views

A primitive polynomial of positive degree is irreducible over D[X] iff it is irreducible over $F[X]$

Published on 16 Apr 2026 - 5:25

205

Views

order of quotient ring $\mathbb{Z}[x]/(x^2+x+1)(x^3+x+1)$

Published on 16 Apr 2026 - 8:17

754

Views

Show that $\mathbb{Z}[\sqrt{-2}]$ is unique factorization domain.

Published on 17 Apr 2026 - 8:16

157

Views

GCD Domain Proof

Published on 30 Apr 2026 - 13:06

3.2k

Views

When is $\mathbb{Z}[\sqrt{d}]$ not an UFD (for $d>1$)?

Published on 13 Apr 2026 - 5:29

List Question

The existence of a specific maximal ideal in a UFD

How to use norms to prove non-UFD?

If an element has prime norm in the ring of quadratic integers, then it is a prime element

What is different $(a_0, a_1, ..., a_d) = (1)$ and $\gcd(a_0, a_1, ..., a_d) = 1$ in arbitrary UFD?

Show for univariate relatively prime polynomials over a perfect field, that $\gcd(fg,(fg)')=\gcd(f,f')\gcd(g,g')$.

Find all discrete valuation subrings of $k(x)$

$f$ has a root in $F$ iff $f$ has a root in $\text{Frac}(F)$

Unique factorization of an element in an UFD

Is $\mathbb{Q}[x,y]/((x+y)^3-2)$ a UFD?

GCD expressed with irreducible elements in a unique factorization domain

A primitive polynomial of positive degree is irreducible over D[X] iff it is irreducible over $F[X]$

order of quotient ring $\mathbb{Z}[x]/(x^2+x+1)(x^3+x+1)$

Show that $\mathbb{Z}[\sqrt{-2}]$ is unique factorization domain.

GCD Domain Proof

When is $\mathbb{Z}[\sqrt{d}]$ not an UFD (for $d>1$)?

Trending Questions

Popular # Hahtags

Popular Questions