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 135 · Answer 1 · 2024-01-29 20:43:26

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 90 · Answer 2 · 2024-02-03 09:43:25

90

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score 29 · Answer 7 · 2024-03-23 21:58:16

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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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