List questions from unique-factorization-domains

Published on 01 Sep 2020 - 19:19

53

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Certain subrings of $k[t]$

Published on 02 Sep 2020 - 19:27

92

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Are $k[x^2,x^3+x]$ and $k[x^3,x^2+x]$ UFD's?

Published on 03 Sep 2020 - 20:57

175

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Is $k[x^2+x,x^3+x]$ a UFD?

Published on 03 Sep 2020 - 23:53

105

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Writing and improving basic divisibility proofs in UFD. (some examples)

Published on 27 Sep 2020 - 1:27

129

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What does it mean that $\mathbb{Q}[x]/(x^2 - x + 15)$ has class number 3?

Published on 12 Oct 2020 - 16:08

56

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Irreducible in $S^{-1}R$ implies numerator irreducible in R?

Published on 14 Oct 2020 - 16:41

253

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Integer rings and UFDs in transcendental field extensions of $\mathbb{Q}$

Published on 25 Mar 2026 - 13:55

116

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Does every pair of non-zero elements of $Z[\sqrt{3}]$ has a gcd?

Published on 27 Mar 2026 - 4:23

169

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Equivalent definitions of Unique Factorization Domain

Published on 25 Oct 2020 - 19:36

27

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If $a$ and $b$ on a UFD don't have any associated irreducible factors, then $1\in GCD(a,b)$

Published on 26 Oct 2020 - 0:14

98

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Isomorphism between posets of ideals of $\mathbb Q[x]$ and $\mathbb Q[x,y]$.

Published on 28 Oct 2020 - 9:12

298

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Prove that $R = \Bbb C \left [X,Y,Z \right ]/ \left \langle 2X^2Y - 3XY^3 + Z \right \rangle$ is a unique factorization domain.

Published on 30 Oct 2020 - 15:44

100

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Show that the ring $\Bbb C[x,y,z]/\langle 2x^2y-5xy^3+z\rangle $ is a UFD

Published on 28 Mar 2026 - 22:31

252

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Fermat's Last Theorem: Complex Polynomials Proof

Published on 12 Nov 2020 - 14:48

List Question

Relation between $k \subsetneq R \subseteq k[x,y]$ being a UFD and $R[y,xy]$ being a UFD

Certain subrings of $k[t]$

Are $k[x^2,x^3+x]$ and $k[x^3,x^2+x]$ UFD's?

Is $k[x^2+x,x^3+x]$ a UFD?

Writing and improving basic divisibility proofs in UFD. (some examples)

What does it mean that $\mathbb{Q}[x]/(x^2 - x + 15)$ has class number 3?

Irreducible in $S^{-1}R$ implies numerator irreducible in R?

Integer rings and UFDs in transcendental field extensions of $\mathbb{Q}$

Does every pair of non-zero elements of $Z[\sqrt{3}]$ has a gcd?

Equivalent definitions of Unique Factorization Domain

If $a$ and $b$ on a UFD don't have any associated irreducible factors, then $1\in GCD(a,b)$

Isomorphism between posets of ideals of $\mathbb Q[x]$ and $\mathbb Q[x,y]$.

Prove that $R = \Bbb C \left [X,Y,Z \right ]/ \left \langle 2X^2Y - 3XY^3 + Z \right \rangle$ is a unique factorization domain.

Show that the ring $\Bbb C[x,y,z]/\langle 2x^2y-5xy^3+z\rangle $ is a UFD

Fermat's Last Theorem: Complex Polynomials Proof

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