Question

Is the ideal $J:=\langle -y^2+xz,x^5-z^3 \rangle$ prime in $\Bbb{C}[x,y,z]?$

score 1.1k · Answer 1 · 2026-04-23 07:59:10

1.1k

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Is the ideal $J:=\langle -y^2+xz,x^5-z^3 \rangle$ prime in $\Bbb{C}[x,y,z]?$

Published on 23 Apr 2026 - 7:59

score 184 · Answer 2 · 2026-04-16 11:16:18

184

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Let $A$ be a ring and $P \subsetneq R \subsetneq Q$ be prime ideals of $A[x]$. The following is not true: $P \cap A= Q \cap A =R \cap A$.

Published on 16 Apr 2026 - 11:16

score 326 · Answer 3 · 2026-05-10 15:29:10

326

Views

Ring with finitely many maximal ideals whose localizations are Noetherian injects into $\bigoplus_{\mathfrak{m}}R_{\mathfrak{m}}$

Published on 10 May 2026 - 15:29

score 97 · Answer 4 · 2026-04-13 03:36:39

97

Views

Which max ideal/kernel of this homomorphism does this correspond to

Published on 13 Apr 2026 - 3:36

score 49 · Answer 5 · 2026-04-15 22:18:16

49

Views

Ideals in Commutative Rings Containing a Field

Published on 15 Apr 2026 - 22:18

score 136 · Answer 6 · 2026-05-07 07:41:02

136

Views

$c_{00}$ is not contained in maximal ideal

Published on 07 May 2026 - 7:41

score 1.3k · Answer 7 · 2026-04-14 16:34:14

1.3k

Views

Let $R$ be a commutative ring with $1\neq 0$. Prove that if every proper ideal of $R$ is prime, then $R$ is a field.

Published on 14 Apr 2026 - 16:34

score 404 · Answer 8 · 2026-04-15 19:11:25

404

Views

Krull dimension of $\mathbb{R}[x_1, \ldots, x_n]/(F)$?

Published on 15 Apr 2026 - 19:11

score 46 · Answer 9 · 2026-04-13 00:32:53

46

Views

Usual argument in algebra?

Published on 13 Apr 2026 - 0:32

score 710 · Answer 10 · 2026-05-10 13:50:18

710

Views

$(x)$ prime ideal in $R[x]$ iff $R$ integral domain by contrapositive

Published on 10 May 2026 - 13:50

score 778 · Answer 11 · 2026-05-10 18:05:17

778

Views

Irreducible affine algebraic varieties corresponds to prime ideals

Published on 10 May 2026 - 18:05

score 2.2k · Answer 12 · 2026-04-13 23:09:38

2.2k

Views

In the proof that an algebraic set $V$ is irreducible iff $I(V)$ is prime.

Published on 13 Apr 2026 - 23:09

score 294 · Answer 13 · 2026-04-14 21:23:12

294

Views

Ideal is maximal iff the zero ideal is maximal in the quotient ring

Published on 14 Apr 2026 - 21:23

score 315 · Answer 14 · 2026-05-10 18:05:18

315

Views

Show that every nonzero prime ideal in $\mathbb{C}[x, y]/(x^2 - y^2 - 1)$ is maximal

Published on 10 May 2026 - 18:05

score 48 · Answer 15 · 2026-05-10 15:02:09

48

Views

How to evaluate $f(x)$ at the point $(x^2 + ax + b) \in \text{Spec} \, \mathbb{R}[x] $?

Published on 10 May 2026 - 15:02

List Question

Is the ideal $J:=\langle -y^2+xz,x^5-z^3 \rangle$ prime in $\Bbb{C}[x,y,z]?$

Let $A$ be a ring and $P \subsetneq R \subsetneq Q$ be prime ideals of $A[x]$. The following is not true: $P \cap A= Q \cap A =R \cap A$.

Ring with finitely many maximal ideals whose localizations are Noetherian injects into $\bigoplus_{\mathfrak{m}}R_{\mathfrak{m}}$

Which max ideal/kernel of this homomorphism does this correspond to

Ideals in Commutative Rings Containing a Field

$c_{00}$ is not contained in maximal ideal

Let $R$ be a commutative ring with $1\neq 0$. Prove that if every proper ideal of $R$ is prime, then $R$ is a field.

Krull dimension of $\mathbb{R}[x_1, \ldots, x_n]/(F)$?

Usual argument in algebra?

$(x)$ prime ideal in $R[x]$ iff $R$ integral domain by contrapositive

Irreducible affine algebraic varieties corresponds to prime ideals

In the proof that an algebraic set $V$ is irreducible iff $I(V)$ is prime.

Ideal is maximal iff the zero ideal is maximal in the quotient ring

Show that every nonzero prime ideal in $\mathbb{C}[x, y]/(x^2 - y^2 - 1)$ is maximal

How to evaluate $f(x)$ at the point $(x^2 + ax + b) \in \text{Spec} \, \mathbb{R}[x] $?

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