Question

Existence of integers $a$ and $b$ such that $p = a^2 +ab+b^2$ for $p = 3 $ or $p\equiv 1 \mod 3$

score 181 · Answer 1 · 2026-02-23 04:02:51

181

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Existence of integers $a$ and $b$ such that $p = a^2 +ab+b^2$ for $p = 3 $ or $p\equiv 1 \mod 3$

Published on 23 Feb 2026 - 4:02

score 535 · Answer 2 · 2026-02-23 04:02:31

535

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Prove that the ideal $I = \left( 3, 2 + \sqrt{-5} \right)$ is a prime ideal in $\mathbb{Z}\left[ \sqrt{-5} \right]$.

Published on 23 Feb 2026 - 4:02

score 1.2k · Answer 3 · 2017-10-12 22:32:49

1.2k

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Prove whether $(5, X^2 + 3) \subseteq \mathbb{Z}[X]$ is a maximum/prime ideal.

Published on 12 Oct 2017 - 22:32

score 452 · Answer 4 · 2017-10-13 19:25:27

452

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How can we find an irreducible (projective) curve of a given degree?

Published on 13 Oct 2017 - 19:25

score 1k · Answer 5 · 2017-10-15 18:01:34

1k

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Maximal ideals of the ring $\frac{K[X,Y]}{\langle XY\rangle}$

Published on 15 Oct 2017 - 18:01

score 47 · Answer 6 · 2017-10-15 19:25:06

47

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Existence of the finitely additive function $2^{\mathbb N}\to\mathbb Z_2$ st. $\{n\}\mapsto 1$

Published on 15 Oct 2017 - 19:25

score 75 · Answer 7 · 2026-03-26 21:35:22

75

Views

On factorisation into prime ideals in a Dedekind domain

Published on 26 Mar 2026 - 21:35

score 1.5k · Answer 8 · 2026-03-28 13:42:04

1.5k

Views

Understanding Ideals and Quotients in Polynomial Rings of Multiple Variables

Published on 28 Mar 2026 - 13:42

score 129 · Answer 9 · 2017-10-17 20:53:15

129

Views

Step in proof: $M$ is a maximal ideal of $R$ iff $R/M$ is a field

Published on 17 Oct 2017 - 20:53

score 164 · Answer 10 · 2026-03-28 20:58:31

164

Views

Intersection of all prime ideals of weakly Noetherian ring

Published on 28 Mar 2026 - 20:58

score 198 · Answer 11 · 2017-10-28 15:15:33

198

Views

Necessary Condition for Prime Ideal in Commutative Ring

Published on 28 Oct 2017 - 15:15

score 242 · Answer 12 · 2017-10-30 16:23:03

242

Views

Rational integer belongs to at most certain number of ideals

Published on 30 Oct 2017 - 16:23

score 84 · Answer 13 · 2017-10-30 20:55:39

84

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Let A be a commutative ring. Let $I \subsetneq A$. Show that there exists a maximal ideal $m \subseteq A$ such that $I \subseteq m$

Published on 30 Oct 2017 - 20:55

score 140 · Answer 14 · 2017-11-05 19:42:15

140

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When does the prime avoidance lemma hold with sum instead of union?

Published on 05 Nov 2017 - 19:42

score 86 · Answer 15 · 2026-03-29 12:05:16

86

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Proving an ideal is prime and calculating dimension of the corresponding quotient ring

Published on 29 Mar 2026 - 12:05

List Question

Existence of integers $a$ and $b$ such that $p = a^2 +ab+b^2$ for $p = 3 $ or $p\equiv 1 \mod 3$

Prove that the ideal $I = \left( 3, 2 + \sqrt{-5} \right)$ is a prime ideal in $\mathbb{Z}\left[ \sqrt{-5} \right]$.

Prove whether $(5, X^2 + 3) \subseteq \mathbb{Z}[X]$ is a maximum/prime ideal.

How can we find an irreducible (projective) curve of a given degree?

Maximal ideals of the ring $\frac{K[X,Y]}{\langle XY\rangle}$

Existence of the finitely additive function $2^{\mathbb N}\to\mathbb Z_2$ st. $\{n\}\mapsto 1$

On factorisation into prime ideals in a Dedekind domain

Understanding Ideals and Quotients in Polynomial Rings of Multiple Variables

Step in proof: $M$ is a maximal ideal of $R$ iff $R/M$ is a field

Intersection of all prime ideals of weakly Noetherian ring

Necessary Condition for Prime Ideal in Commutative Ring

Rational integer belongs to at most certain number of ideals

Let A be a commutative ring. Let $I \subsetneq A$. Show that there exists a maximal ideal $m \subseteq A$ such that $I \subseteq m$

When does the prime avoidance lemma hold with sum instead of union?

Proving an ideal is prime and calculating dimension of the corresponding quotient ring

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