List questions from unique-factorization-domains

Published on 26 Mar 2026 - 16:04

126

Views

$A[X, Y ]/(X^2+Y^2−1)$ is integral domain

Published on 26 Mar 2026 - 19:17

62

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Characterization of irreducible multivariate polynomials over the complex numbers

Published on 25 Mar 2026 - 9:25

56

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Is there a general formula for factorizing multivariate complex polynomials?

Published on 25 Mar 2026 - 9:33

58

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Proving existence of a lcm in a Unique Factorization Domain $D$ using the ascending chain condition?

Published on 06 May 2023 - 22:53

111

Views

$\mathbb Z[x_n]$ is always a UFD?

Published on 18 May 2023 - 20:25

26

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Primes in quadratic rings that are not UFD's

Published on 23 Feb 2026 - 8:32

120

Views

The diophantine equation $ a^2 + p b^2 = c^2 + p d^2 = q $ and related ring theory questions.

Published on 20 Jun 2023 - 22:19

35

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Do all polynomials $p(x)$ with integer coefficients output infinitely many composite numbers for integer $x$?

Published on 07 Jul 2023 - 17:09

78

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Factorization of $x^3-10x+4$ over $\mathbb Q(\sqrt 2, \sqrt[3] 2)$

Published on 16 Jul 2023 - 19:40

30

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Divisibility of a non invertible element in an integral domain

Published on 26 Jul 2023 - 18:46

31

Views

$c(kp) = kc(p)$ where $c$ is the content of a polynomial, $p$ a polynomial in $R[x]$ and $k \in R-\{0\}$ (without assuming Gauss' Lemma)

Published on 09 Aug 2023 - 21:17

27

Views

For compact and connected $K\subset\mathbb{C}$, $H(K)$ is a PID?

Published on 22 Aug 2023 - 15:48

62

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Why $y$ is a rational integer?

Published on 29 Sep 2023 - 23:31

92

Views

Deducing that $\mathbb Z[2 \sqrt{2}]$ is not a $UFD.$

Published on 25 Mar 2026 - 11:53

List Question

Multiplicative Subsets of the Natural Numbers and Unique Factorization

$A[X, Y ]/(X^2+Y^2−1)$ is integral domain

Characterization of irreducible multivariate polynomials over the complex numbers

Is there a general formula for factorizing multivariate complex polynomials?

Proving existence of a lcm in a Unique Factorization Domain $D$ using the ascending chain condition?

$\mathbb Z[x_n]$ is always a UFD?

Primes in quadratic rings that are not UFD's

The diophantine equation $ a^2 + p b^2 = c^2 + p d^2 = q $ and related ring theory questions.

Do all polynomials $p(x)$ with integer coefficients output infinitely many composite numbers for integer $x$?

Factorization of $x^3-10x+4$ over $\mathbb Q(\sqrt 2, \sqrt[3] 2)$

Divisibility of a non invertible element in an integral domain

$c(kp) = kc(p)$ where $c$ is the content of a polynomial, $p$ a polynomial in $R[x]$ and $k \in R-\{0\}$ (without assuming Gauss' Lemma)

For compact and connected $K\subset\mathbb{C}$, $H(K)$ is a PID?

Why $y$ is a rational integer?

Deducing that $\mathbb Z[2 \sqrt{2}]$ is not a $UFD.$

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