Question

How does Euclidean Domain imply Unique Factorization domain for Gaussian Integers?

score 1k · Answer 1 · 2026-03-26 04:32:44

1k

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How does Euclidean Domain imply Unique Factorization domain for Gaussian Integers?

Published on 26 Mar 2026 - 4:32

score 300 · Answer 2 · 2017-05-11 13:22:46

300

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A simple algebraic ring extension of a UFD having no prime elements

Published on 11 May 2017 - 13:22

score 478 · Answer 3 · 2017-05-11 23:42:19

478

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Prime elements of $\mathbb{C}[x]$ which remain prime in a simple algebraic ring extension

Published on 11 May 2017 - 23:42

score 66 · Answer 4 · 2017-05-15 10:59:36

66

Views

If $x = y^3$ in $\mathbb{Z} + \frac{-1 + \sqrt{-3}}{2}\mathbb{Z}$, then there is some $w \in \mathbb{Z} + \sqrt{-3}\mathbb{Z}$ such that $x = w^3$.

Published on 15 May 2017 - 10:59

score 135 · Answer 5 · 2017-05-15 16:29:03

135

Views

showing elements in $\mathbb{Z}+\frac{1 + \sqrt{5}}{2}\mathbb{Z}$ are associated

Published on 15 May 2017 - 16:29

score 74 · Answer 6 · 2017-05-16 14:40:30

74

Views

Factoring $a + b\frac{1 + \sqrt{5}}{2}$ if $a^2 + ab - b^2 = a+b$

Published on 16 May 2017 - 14:40

score 751 · Answer 7 · 2017-05-17 08:27:33

751

Views

What is the complexity of multivariate gcd?

Published on 17 May 2017 - 8:27

score 641 · Answer 8 · 2026-03-28 10:17:14

641

Views

Problem with definition of unique factorization domain (UFD)

Published on 28 Mar 2026 - 10:17

score 134 · Answer 9 · 2017-05-18 09:33:17

134

Views

Proving that $a+b\sqrt{-3}$ is a cube if $a^2 + 3b^2 = c^3$

Published on 18 May 2017 - 9:33

score 257 · Answer 10 · 2017-05-18 22:40:09

257

Views

Background to learn Auslander-Buchsbaum factoriality theorem

Published on 18 May 2017 - 22:40

score 150 · Answer 11 · 2017-05-22 19:16:33

150

Views

Find all ideals $\mathbb{Z}[x,y]$ such that the corresponding factor ring is a UFD

Published on 22 May 2017 - 19:16

score 193 · Answer 12 · 2026-03-28 13:41:53

193

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When is every prime element of a Noetherian UFD irreducible in a simple algebraic ring extension

Published on 28 Mar 2026 - 13:41

score 1.3k · Answer 13 · 2017-05-25 17:23:45

1.3k

Views

When a polynomial in two variables of (total) degree three is irreducible?

Published on 25 May 2017 - 17:23

score 184 · Answer 14 · 2026-03-28 10:16:29

184

Views

Showing that an element of a polynomial ring is irreducible

Published on 28 Mar 2026 - 10:16

score 845 · Answer 15 · 2017-05-31 19:31:21

845

Views

Example for Noetherian domain, non-UFD $R$ of dimension one such that every localization $R_P$ is UFD.

Published on 31 May 2017 - 19:31

List Question

How does Euclidean Domain imply Unique Factorization domain for Gaussian Integers?

A simple algebraic ring extension of a UFD having no prime elements

Prime elements of $\mathbb{C}[x]$ which remain prime in a simple algebraic ring extension

If $x = y^3$ in $\mathbb{Z} + \frac{-1 + \sqrt{-3}}{2}\mathbb{Z}$, then there is some $w \in \mathbb{Z} + \sqrt{-3}\mathbb{Z}$ such that $x = w^3$.

showing elements in $\mathbb{Z}+\frac{1 + \sqrt{5}}{2}\mathbb{Z}$ are associated

Factoring $a + b\frac{1 + \sqrt{5}}{2}$ if $a^2 + ab - b^2 = a+b$

What is the complexity of multivariate gcd?

Problem with definition of unique factorization domain (UFD)

Proving that $a+b\sqrt{-3}$ is a cube if $a^2 + 3b^2 = c^3$

Background to learn Auslander-Buchsbaum factoriality theorem

Find all ideals $\mathbb{Z}[x,y]$ such that the corresponding factor ring is a UFD

When is every prime element of a Noetherian UFD irreducible in a simple algebraic ring extension

When a polynomial in two variables of (total) degree three is irreducible?

Showing that an element of a polynomial ring is irreducible

Example for Noetherian domain, non-UFD $R$ of dimension one such that every localization $R_P$ is UFD.

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