Question

Every module over a field is free. Is every commutative ring whose modules are all free a field?

score 4.2k · Answer 1 · 2026-04-12 16:45:12

4.2k

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Every module over a field is free. Is every commutative ring whose modules are all free a field?

Published on 12 Apr 2026 - 16:45

score 237 · Answer 2 · 2014-03-19 14:50:27

237

Views

Why is $f'(x)$ the annihilator of $dx$?

Published on 19 Mar 2014 - 14:50

score 130 · Answer 3 · 2026-04-13 19:46:09

130

Views

Problem related to prime ideals of B and A where B is integral over A

Published on 13 Apr 2026 - 19:46

score 114 · Answer 4 · 2026-04-13 15:30:59

114

Views

Describing a locally free sheaf sitting between two locally free sheaves which are given as extensions

Published on 13 Apr 2026 - 15:30

score 59 · Answer 5 · 2026-04-13 11:14:29

59

Views

Could you please explain the detail of the proof

Published on 13 Apr 2026 - 11:14

score 73 · Answer 6 · 2014-03-19 19:08:01

73

Views

proving that the height of $(X)$ in $R[X]$ is equal to 1

Published on 19 Mar 2014 - 19:08

score 67 · Answer 7 · 2026-04-13 16:30:02

67

Views

Showing two thing are isomorphic as $k$-algebras

Published on 13 Apr 2026 - 16:30

score 826 · Answer 8 · 2026-04-01 04:36:19

826

Views

Hilbert-Burch theorem characterizes perfect ideals of grade $2$

Published on 01 Apr 2026 - 4:36

score 200 · Answer 9 · 2026-04-13 06:29:28

200

Views

proving an isomorphism of direct limits

Published on 13 Apr 2026 - 6:29

score 451 · Answer 10 · 2026-04-13 10:50:49

451

Views

Relation between closed subschemes and saturated ideals

Published on 13 Apr 2026 - 10:50

score 61 · Answer 11 · 2026-04-13 15:24:07

61

Views

How can we show that $\operatorname{Tor}_1^A(\hat{A},G_f/G)=0$?

Published on 13 Apr 2026 - 15:24

score 216 · Answer 12 · 2026-04-09 16:16:57

216

Views

Proposition 3.5.1 in Bruns and Herzog, Cohen-Macaulay Rings

Published on 09 Apr 2026 - 16:16

score 129 · Answer 13 · 2026-04-10 12:32:03

129

Views

Find the projective closure of the ideal $I=\langle y-x^2,z-x^3\rangle$

Published on 10 Apr 2026 - 12:32

score 2.4k · Answer 14 · 2026-04-13 21:22:28

2.4k

Views

Tensor product of quotient rings : A proof using Yoneda lemma

Published on 13 Apr 2026 - 21:22

score 353 · Answer 15 · 2026-04-11 19:27:26

353

Views

$Z(I:J)$ is the Zariski closure of $Z(I)-Z(J)$

Published on 11 Apr 2026 - 19:27

List Question

Every module over a field is free. Is every commutative ring whose modules are all free a field?

Why is $f'(x)$ the annihilator of $dx$?

Problem related to prime ideals of B and A where B is integral over A

Describing a locally free sheaf sitting between two locally free sheaves which are given as extensions

Could you please explain the detail of the proof

proving that the height of $(X)$ in $R[X]$ is equal to 1

Showing two thing are isomorphic as $k$-algebras

Hilbert-Burch theorem characterizes perfect ideals of grade $2$

proving an isomorphism of direct limits

Relation between closed subschemes and saturated ideals

How can we show that $\operatorname{Tor}_1^A(\hat{A},G_f/G)=0$?

Proposition 3.5.1 in Bruns and Herzog, Cohen-Macaulay Rings

Find the projective closure of the ideal $I=\langle y-x^2,z-x^3\rangle$

Tensor product of quotient rings : A proof using Yoneda lemma

$Z(I:J)$ is the Zariski closure of $Z(I)-Z(J)$

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