Question

$\Bbb R[X,Y]/(F) \cong \Bbb R[Z]$ and $F_X G_Y - G_X F_Y \in \Bbb R^*$

score 977 · Answer 1 · 2026-03-25 07:45:36

977

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$\Bbb R[X,Y]/(F) \cong \Bbb R[Z]$ and $F_X G_Y - G_X F_Y \in \Bbb R^*$

Published on 25 Mar 2026 - 7:45

score 1.6k · Answer 2 · 2026-03-25 06:05:04

1.6k

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Given any commutative ring $R$ with unity, $R[X]$ has infinitely many maximal ideals.

Published on 25 Mar 2026 - 6:05

score 237 · Answer 3 · 2026-03-25 01:37:49

237

Views

Finding a basis of a $\mathbb{Z}[i]$-submodule of $\mathbb{Z}[i]^2$ given by generators

Published on 25 Mar 2026 - 1:37

score 74 · Answer 4 · 2018-08-27 09:08:21

74

Views

x^3=x implies R commutative (Motivation)

Published on 27 Aug 2018 - 9:08

score 52 · Answer 5 · 2018-08-27 16:03:11

52

Views

About field of fractions and their classification in the case of $K\left(\eta\right)$

Published on 27 Aug 2018 - 16:03

score 432 · Answer 6 · 2018-08-28 00:42:22

432

Views

Elementary proof of $\mathcal{O}_K$ is a free abelian group of rank $n$

Published on 28 Aug 2018 - 0:42

score 161 · Answer 7 · 2018-08-28 14:34:37

161

Views

ring contains a subring isomorphic to $Z$ implies it is integral domain?

Published on 28 Aug 2018 - 14:34

score 380 · Answer 8 · 2026-03-29 07:00:27

380

Views

Am I right to say that "integrally closed extension" and "algebraically closed extension" don't agree in their meaning, even for field extensions?

Published on 29 Mar 2026 - 7:00

score 553 · Answer 9 · 2018-08-29 22:26:58

553

Views

Vakil 3.2.P - Morphism between Spec induced by Ring Morphism

Published on 29 Aug 2018 - 22:26

score 59 · Answer 10 · 2026-03-28 08:35:36

59

Views

Radical of the ideal $I^2$ is a maximal ideal.

Published on 28 Mar 2026 - 8:35

score 245 · Answer 11 · 2026-03-28 12:55:53

245

Views

$R$-module $R=\mathbb{Z}[\sqrt{-2}]$

Published on 28 Mar 2026 - 12:55

score 155 · Answer 12 · 2018-08-31 13:01:57

155

Views

Examples of primitive rings containing some, but not all, finite rank operators

Published on 31 Aug 2018 - 13:01

score 28 · Answer 13 · 2018-08-31 16:44:24

28

Views

Special decomposition of polymonial from $R[x]$, where $R$-UFD

Published on 31 Aug 2018 - 16:44

score 1.2k · Answer 14 · 2018-08-31 21:56:28

$p(x)$ is a unit in $R[x]$ where $R$ is a general unity ring if and only if it's constant term is a unit and all other coefficients are nilpotent

score 8.4k · Answer 15 · 2018-09-01 01:13:40

8.4k

Views

$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$

Published on 01 Sep 2018 - 1:13

List Question

$\Bbb R[X,Y]/(F) \cong \Bbb R[Z]$ and $F_X G_Y - G_X F_Y \in \Bbb R^*$

Given any commutative ring $R$ with unity, $R[X]$ has infinitely many maximal ideals.

Finding a basis of a $\mathbb{Z}[i]$-submodule of $\mathbb{Z}[i]^2$ given by generators

x^3=x implies R commutative (Motivation)

About field of fractions and their classification in the case of $K\left(\eta\right)$

Elementary proof of $\mathcal{O}_K$ is a free abelian group of rank $n$

ring contains a subring isomorphic to $Z$ implies it is integral domain?

Am I right to say that "integrally closed extension" and "algebraically closed extension" don't agree in their meaning, even for field extensions?

Vakil 3.2.P - Morphism between Spec induced by Ring Morphism

Radical of the ideal $I^2$ is a maximal ideal.

$R$-module $R=\mathbb{Z}[\sqrt{-2}]$

Examples of primitive rings containing some, but not all, finite rank operators

Special decomposition of polymonial from $R[x]$, where $R$-UFD

$p(x)$ is a unit in $R[x]$ where $R$ is a general unity ring if and only if it's constant term is a unit and all other coefficients are nilpotent

$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$

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