Question

For ring map $R\longrightarrow S$, if $I$ is injective $R$-module, is $Hom_R(S,I)$ an injective $S$-module?

score 117 · Answer 1 · 2018-09-20 01:00:44

117

Views

For ring map $R\longrightarrow S$, if $I$ is injective $R$-module, is $Hom_R(S,I)$ an injective $S$-module?

Published on 20 Sep 2018 - 1:00

score 217 · Answer 2 · 2018-09-20 05:39:07

217

Views

All rings $A$ between $\mathbb{Z}$ and $\mathbb{Q}$

Published on 20 Sep 2018 - 5:39

score 166 · Answer 3 · 2026-03-25 22:04:18

166

Views

Is there a fixed-point theorem that can be applied to a ring endomorphism of $k[x,y]$?

Published on 25 Mar 2026 - 22:04

score 332 · Answer 4 · 2018-09-21 04:32:48

332

Views

Intuition behind why being integral over a ring is important

Published on 21 Sep 2018 - 4:32

score 173 · Answer 5 · 2018-09-21 19:52:53

173

Views

Uniqueness of Isomorphism $M \otimes_A N \cong N \otimes_A M$ (Proposition 2.14 in Atiyah-Macdonald).

Published on 21 Sep 2018 - 19:52

score 320 · Answer 6 · 2026-03-25 23:11:12

320

Views

Are morphisms of schemes determined by morphisms of $A$-valued points where $A$ is an affine scheme?

Published on 25 Mar 2026 - 23:11

score 276 · Answer 7 · 2026-03-23 00:38:53

276

Views

Example of a characteristic zero local ring with a quotient of positive characteristic

Published on 23 Mar 2026 - 0:38

score 801 · Answer 8 · 2018-09-22 01:20:15

Show that $\dim_k(\mathfrak m^n / \mathfrak m^{n+1})=n+1$ whenever $0\leq n<m_P$, where $(\mathcal O,\mathfrak m)$ is the local ring of $P$

score 309 · Answer 9 · 2018-09-22 09:54:04

309

Views

Support of a module

Published on 22 Sep 2018 - 9:54

score 52 · Answer 10 · 2026-03-29 10:15:15

52

Views

Help calculating ideal generated by the union of two ideals

Published on 29 Mar 2026 - 10:15

score 49 · Answer 11 · 2026-03-25 23:38:06

49

Views

construct a closed subspace of $\mathcal{HS}(H)$ such that all elements in the subspace are commutative.

Published on 25 Mar 2026 - 23:38

score 1.5k · Answer 12 · 2026-03-25 23:09:42

1.5k

Views

Smooth and Regular Schemes

Published on 25 Mar 2026 - 23:09

score 2.8k · Answer 13 · 2018-09-23 18:48:08

2.8k

Views

Krull Intersection Theorem

Published on 23 Sep 2018 - 18:48

score 372 · Answer 14 · 2026-03-25 12:17:13

372

Views

Exercise 1.8 from Hartshorne

Published on 25 Mar 2026 - 12:17

score 45 · Answer 15 · 2026-03-26 01:12:11

45

Views

If the images of $m_1, \dots, m_r$ in $S^{-1}M$ generate the module, then so do their images in $M_f$, for some $f \in S$.

Published on 26 Mar 2026 - 1:12

List Question

For ring map $R\longrightarrow S$, if $I$ is injective $R$-module, is $Hom_R(S,I)$ an injective $S$-module?

All rings $A$ between $\mathbb{Z}$ and $\mathbb{Q}$

Is there a fixed-point theorem that can be applied to a ring endomorphism of $k[x,y]$?

Intuition behind why being integral over a ring is important

Uniqueness of Isomorphism $M \otimes_A N \cong N \otimes_A M$ (Proposition 2.14 in Atiyah-Macdonald).

Are morphisms of schemes determined by morphisms of $A$-valued points where $A$ is an affine scheme?

Example of a characteristic zero local ring with a quotient of positive characteristic

Show that $\dim_k(\mathfrak m^n / \mathfrak m^{n+1})=n+1$ whenever $0\leq n<m_P$, where $(\mathcal O,\mathfrak m)$ is the local ring of $P$

Support of a module

Help calculating ideal generated by the union of two ideals

construct a closed subspace of $\mathcal{HS}(H)$ such that all elements in the subspace are commutative.

Smooth and Regular Schemes

Krull Intersection Theorem

Exercise 1.8 from Hartshorne

If the images of $m_1, \dots, m_r$ in $S^{-1}M$ generate the module, then so do their images in $M_f$, for some $f \in S$.

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