Question

Prove $(y-x^2)$ is a prime ideal in $\mathbb{R}[x,y]$, but not maximal.

score 1.3k · Answer 1 · 2026-03-29 13:40:56

1.3k

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Prove $(y-x^2)$ is a prime ideal in $\mathbb{R}[x,y]$, but not maximal.

Published on 29 Mar 2026 - 13:40

score 286 · Answer 2 · 2026-03-25 17:45:21

286

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About the concept of a valuation ring

Published on 25 Mar 2026 - 17:45

score 1.5k · Answer 3 · 2026-03-30 22:47:22

1.5k

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MacLane-Birkhoff's "Algebra" vs Jacobson's "Basic Algebra I,II" vs Lang's "Algebra"

Published on 30 Mar 2026 - 22:47

score 152 · Answer 4 · 2019-05-26 04:55:11

152

Views

All left ideals in ring $R$ are trivial, and there are two elements whose product is nonzero. Prove that $R$ forms a skew field.

Published on 26 May 2019 - 4:55

score 135 · Answer 5 · 2019-05-26 08:07:35

135

Views

A prime ideal $P$ contains a minimal prime ideal for any ideal $I \subset P$.

Published on 26 May 2019 - 8:07

score 266 · Answer 6 · 2026-03-25 14:39:19

266

Views

Rings for which the Köthe conjecture holds

Published on 25 Mar 2026 - 14:39

score 54 · Answer 7 · 2026-04-07 11:29:04

54

Views

Prove that there exists a polynomial $p(x) \in \mathbb{Q}[x]$ of degree 21 such that $p(5^{1/3}+7^{1/7})=0$

Published on 07 Apr 2026 - 11:29

score 53 · Answer 8 · 2019-05-26 20:37:35

53

Views

Give the description of all commutative rings with unity of $8$ elements

Published on 26 May 2019 - 20:37

score 598 · Answer 9 · 2026-03-25 09:25:17

598

Views

Show that this domain is integrally closed

Published on 25 Mar 2026 - 9:25

score 48 · Answer 10 · 2019-05-26 21:15:07

48

Views

Quotient of free module is still free

Published on 26 May 2019 - 21:15

score 560 · Answer 11 · 2026-03-26 02:56:26

560

Views

Let $I$ be an ideal of a ring $(R,+,\cdot)$. Prove that the quotient homomorphism $\varphi : R \rightarrow R / I$ is a ring homomorphism

Published on 26 Mar 2026 - 2:56

score 175 · Answer 12 · 2019-05-27 08:05:36

175

Views

All integers $m$ satisfying $m\equiv n^2 \mod 19$

Published on 27 May 2019 - 8:05

score 1.6k · Answer 13 · 2019-05-27 08:57:17

1.6k

Views

<p> is a prime ideal iff p is a prime (integral domain)

Published on 27 May 2019 - 8:57

score 810 · Answer 14 · 2026-03-29 15:40:28

810

Views

Ideals of $R[x]/I[x]$, where $I$ is a maximal ideal of $R$

Published on 29 Mar 2026 - 15:40

score 66 · Answer 15 · 2019-05-27 17:11:09

66

Views

Prove $S/\operatorname{Ker}(\alpha) \cong (\operatorname{Im}\alpha)$ where $\alpha: S \rightarrow T$ is a ring homomorphism

Published on 27 May 2019 - 17:11

List Question

Prove $(y-x^2)$ is a prime ideal in $\mathbb{R}[x,y]$, but not maximal.

About the concept of a valuation ring

MacLane-Birkhoff's "Algebra" vs Jacobson's "Basic Algebra I,II" vs Lang's "Algebra"

All left ideals in ring $R$ are trivial, and there are two elements whose product is nonzero. Prove that $R$ forms a skew field.

A prime ideal $P$ contains a minimal prime ideal for any ideal $I \subset P$.

Rings for which the Köthe conjecture holds

Prove that there exists a polynomial $p(x) \in \mathbb{Q}[x]$ of degree 21 such that $p(5^{1/3}+7^{1/7})=0$

Give the description of all commutative rings with unity of $8$ elements

Show that this domain is integrally closed

Quotient of free module is still free

Let $I$ be an ideal of a ring $(R,+,\cdot)$. Prove that the quotient homomorphism $\varphi : R \rightarrow R / I$ is a ring homomorphism

All integers $m$ satisfying $m\equiv n^2 \mod 19$

<p> is a prime ideal iff p is a prime (integral domain)

Ideals of $R[x]/I[x]$, where $I$ is a maximal ideal of $R$

Prove $S/\operatorname{Ker}(\alpha) \cong (\operatorname{Im}\alpha)$ where $\alpha: S \rightarrow T$ is a ring homomorphism

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