Question

If $f:R\to S$ is a surjective homomorphism of integral domains, $p$ is irreducible in $R,$ and $f(p)\neq 0_R$ is $f(p)$ irreducible in $S?$

score 138 · Answer 1 · 2026-04-17 15:36:53

If $f:R\to S$ is a surjective homomorphism of integral domains, $p$ is irreducible in $R,$ and $f(p)\neq 0_R$ is $f(p)$ irreducible in $S?$

score 93 · Answer 2 · 2026-04-10 21:01:26

93

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score 60 · Answer 3 · 2026-03-26 01:11:58

60

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score 69 · Answer 4 · 2026-04-13 23:51:09

69

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showing that $\mathbb Z [\sqrt{14}]$ is not euclidean regarding usual norm using only 2 and 1 + $\sqrt{14}$.

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score 39 · Answer 5 · 2026-04-16 00:22:52

39

Views

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score 52 · Answer 6 · 2026-04-15 06:09:07

52

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score 32 · Answer 7 · 2026-04-13 17:07:27

32

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score 49 · Answer 8 · 2026-04-11 18:28:24

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score 1.7k · Answer 10 · 2026-04-11 23:26:32

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score 420 · Answer 11 · 2026-04-05 14:12:41

420

Views

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score 1.6k · Answer 12 · 2026-03-26 22:37:41

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score 1.2k · Answer 13 · 2026-04-14 14:16:09

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score 32.7k · Answer 14 · 2026-03-26 06:10:29

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score 327 · Answer 15 · 2026-04-16 15:08:59

327

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List Question

If $f:R\to S$ is a surjective homomorphism of integral domains, $p$ is irreducible in $R,$ and $f(p)\neq 0_R$ is $f(p)$ irreducible in $S?$

Problem in understanding the unique factorization theorem for Euclidean Rings.

Need help in understanding a proof of the fact: The set of Gaussian integers is a euclidean domain.

showing that $\mathbb Z [\sqrt{14}]$ is not euclidean regarding usual norm using only 2 and 1 + $\sqrt{14}$.

Factorizaton in an Euclidean ring

If $a$ and $b$ are coprimes in an euclidean domain, then $a^n$ and $b$ are coprimes.

polynomials with leading coefficient unit are cancellable?

Construction of connected set in expanded complex plane

Definition of Euclidean domain

Let $ I $ be an ideal in $\mathbb Z [i]$. Show that $\mathbb Z[i] /I $ is finite.

Examples of nonstandard Euclidean functions on Euclidean domain

Euclidean Domain, Associates

On a PID that is not an Euclidean domain

Prove that the Gaussian Integer's ring is a Euclidean domain

Uniqueness of "Euclidean Expressions" in Euclidean Domains

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