Question

Torsion-free $R$-module of rank $1$ is either cyclic or injective

score 498 · Answer 1 · 2026-04-16 19:20:11

498

Views

Torsion-free $R$-module of rank $1$ is either cyclic or injective

Published on 16 Apr 2026 - 19:20

score 188 · Answer 2 · 2026-03-25 16:02:17

188

Views

Local ring with principal maximal ideal and $\cap_{n>0}\mathfrak{m}^n=\{0\}$ is Noetherian?

Published on 25 Mar 2026 - 16:02

score 250 · Answer 3 · 2026-04-11 19:20:06

250

Views

Are epimorphic endomorphisms of noetherian commutative rings always injective?

Published on 11 Apr 2026 - 19:20

score 220 · Answer 4 · 2026-05-02 12:28:17

220

Views

Socle and minimal number of generators of an ideal in a regular local ring

Published on 02 May 2026 - 12:28

score 182 · Answer 5 · 2026-04-12 11:03:10

182

Views

$\mathbb{R}$ is not a variety when considered as a subset of $\mathbb{C}$

Published on 12 Apr 2026 - 11:03

score 64 · Answer 6 · 2026-03-25 17:41:53

64

Views

How to show two rings $(A_f)_{g'}$ and $A_{f g''}$, where $g' = g''/f^n$, are isomorphic?

Published on 25 Mar 2026 - 17:41

score 169 · Answer 7 · 2026-04-16 00:30:55

169

Views

Prove identity $\operatorname{Supp}(M/tM)= \operatorname{Supp}(M) \cap V(tA)$ between supports

Published on 16 Apr 2026 - 0:30

score 111 · Answer 8 · 2026-04-10 04:37:28

111

Views

When can a ring be isomorphic to a quotient of itself?

Published on 10 Apr 2026 - 4:37

score 112 · Answer 9 · 2026-04-08 20:30:33

112

Views

Extension of Scalars is a pseudofunctor

Published on 08 Apr 2026 - 20:30

score 72 · Answer 10 · 2026-03-25 13:57:02

72

Views

Galois extension of local fields with a separable extension of residue fields of positive characteristic

Published on 25 Mar 2026 - 13:57

score 125 · Answer 11 · 2026-03-27 01:04:20

125

Views

Show that there is no proper ideal of finite presentation of $R$.

Published on 27 Mar 2026 - 1:04

score 71 · Answer 12 · 2026-04-15 14:28:11

71

Views

Long exact sequence of derived functors from a finite exact sequence (resolution) ending with zeros

Published on 15 Apr 2026 - 14:28

score 155 · Answer 13 · 2026-05-04 22:08:33

155

Views

Definition of differential forms from derivations

Published on 04 May 2026 - 22:08

score 267 · Answer 14 · 2026-04-11 07:17:43

267

Views

Endomorphism ring of module quotient radical

Published on 11 Apr 2026 - 7:17

score 673 · Answer 15 · 2026-04-13 10:27:30

673

Views

Torsion-free module over a DVR

Published on 13 Apr 2026 - 10:27

List Question

Torsion-free $R$-module of rank $1$ is either cyclic or injective

Local ring with principal maximal ideal and $\cap_{n>0}\mathfrak{m}^n=\{0\}$ is Noetherian?

Are epimorphic endomorphisms of noetherian commutative rings always injective?

Socle and minimal number of generators of an ideal in a regular local ring

$\mathbb{R}$ is not a variety when considered as a subset of $\mathbb{C}$

How to show two rings $(A_f)_{g'}$ and $A_{f g''}$, where $g' = g''/f^n$, are isomorphic?

Prove identity $\operatorname{Supp}(M/tM)= \operatorname{Supp}(M) \cap V(tA)$ between supports

When can a ring be isomorphic to a quotient of itself?

Extension of Scalars is a pseudofunctor

Galois extension of local fields with a separable extension of residue fields of positive characteristic

Show that there is no proper ideal of finite presentation of $R$.

Long exact sequence of derived functors from a finite exact sequence (resolution) ending with zeros

Definition of differential forms from derivations

Endomorphism ring of module quotient radical

Torsion-free module over a DVR

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