Question

Categorical proof of direct sum preserving exactness

score 1.1k · Answer 1 · 2026-03-28 06:15:50

1.1k

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Categorical proof of direct sum preserving exactness

Published on 28 Mar 2026 - 6:15

score 627 · Answer 2 · 2018-07-04 20:37:32

627

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Why is the dimension of a ring, with finite spectrum, $\leq 1$?

Published on 04 Jul 2018 - 20:37

score 45 · Answer 3 · 2026-03-25 10:59:00

45

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The forms of $f,g \in k[x,y]$ such that $k[f,g,x]=k[x,y]$

Published on 25 Mar 2026 - 10:59

score 59 · Answer 4 · 2018-07-07 14:25:50

Given $x\in R$, $R$ a commutative ring, what is the difference between $R/(x)$ and $coker(R\rightarrow^{*x} R)$ and how do I visualize the latter?

score 164 · Answer 5 · 2018-07-08 11:38:05

164

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Does the converse of Krull’s principal ideal theorem hold?

Published on 08 Jul 2018 - 11:38

score 165 · Answer 6 · 2026-03-25 03:21:24

165

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Is $\underset{i}\varprojlim R/(I+J)^i \cong \underset{i}\varprojlim \left( \underset{j}\varprojlim R/(I^i + J^j)\right)$?

Published on 25 Mar 2026 - 3:21

score 807 · Answer 7 · 2018-07-09 06:53:37

807

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Length and dimension of a module

Published on 09 Jul 2018 - 6:53

score 348 · Answer 8 · 2026-03-25 07:49:24

348

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Why do we want Dedekind rings to be integral closed?

Published on 25 Mar 2026 - 7:49

score 1.3k · Answer 9 · 2026-03-25 10:31:40

1.3k

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Ideal is graded iff it is generated by homogeneous elements

Published on 25 Mar 2026 - 10:31

score 1.3k · Answer 10 · 2026-03-25 23:13:10

1.3k

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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 25 Mar 2026 - 23:13

score 352 · Answer 11 · 2026-02-27 16:20:10

352

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Jacobson radical of the $\mathbb{k}$-algebra $\mathbb{k}[x]/\langle x^n\rangle$ where $\mathbb{k}$ is a field

Published on 27 Feb 2026 - 16:20

score 728 · Answer 12 · 2018-07-10 13:36:56

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about graded free $R$-module

Published on 10 Jul 2018 - 13:36

score 117 · Answer 13 · 2026-03-29 03:21:36

117

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Is $R^I$ $\overline{I}$-adically complete?

Published on 29 Mar 2026 - 3:21

score 52 · Answer 14 · 2026-03-23 09:24:20

52

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Showing $I:\langle v_j \rangle \subseteq \langle \{ u_i / \gcd(u_i,v_j) \ : \ i=1,\dots, r \} \rangle$, where $I=\langle u_1, \dots, u_r \rangle$

Published on 23 Mar 2026 - 9:24

score 402 · Answer 15 · 2026-03-25 23:10:12

402

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

Published on 25 Mar 2026 - 23:10

List Question

Categorical proof of direct sum preserving exactness

Why is the dimension of a ring, with finite spectrum, $\leq 1$?

The forms of $f,g \in k[x,y]$ such that $k[f,g,x]=k[x,y]$

Given $x\in R$, $R$ a commutative ring, what is the difference between $R/(x)$ and $coker(R\rightarrow^{*x} R)$ and how do I visualize the latter?

Does the converse of Krull’s principal ideal theorem hold?

Is $\underset{i}\varprojlim R/(I+J)^i \cong \underset{i}\varprojlim \left( \underset{j}\varprojlim R/(I^i + J^j)\right)$?

Length and dimension of a module

Why do we want Dedekind rings to be integral closed?

Ideal is graded iff it is generated by homogeneous elements

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.

Jacobson radical of the $\mathbb{k}$-algebra $\mathbb{k}[x]/\langle x^n\rangle$ where $\mathbb{k}$ is a field

about graded free $R$-module

Is $R^I$ $\overline{I}$-adically complete?

Showing $I:\langle v_j \rangle \subseteq \langle \{ u_i / \gcd(u_i,v_j) \ : \ i=1,\dots, r \} \rangle$, where $I=\langle u_1, \dots, u_r \rangle$

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

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