List questions from local-rings

Published on 25 Mar 2026 - 3:02

156

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Existence of system of parameters via prime avoidance

Published on 23 Apr 2020 - 13:40

53

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How much information about $R$ is encoded in its local rings OR in its tangent spaces if I know the topology of $\operatorname{Spec}(R)$?

Published on 04 May 2020 - 21:10

100

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Dual of a module of finite projective dimension

Published on 06 May 2020 - 17:05

363

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If in a commutative ring $R$ a maximal ideal is nilpotent, then $R$ is local

Published on 10 May 2020 - 23:56

111

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Equality in proof of Theorem 14.9 from Harris's book

Published on 13 May 2020 - 7:56

132

Views

Cancelling the canonical module in tensor products

Published on 14 May 2020 - 11:00

297

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Does the category of local rings with residue field $F$ have an initial object?

Published on 24 Mar 2026 - 3:21

57

Views

Is $(\mathbb{Z}/2\mathbb{Z})[T,T^{-1}]$ a DVR?

Published on 16 May 2020 - 20:02

928

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Prove: $R$ is local $\iff$ $R$ has exactly one maximal ideal.

Published on 25 May 2020 - 11:48

220

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$R$ be local and suppose $x ∈ R$ satisfies $x^2 = x$

Published on 25 May 2020 - 12:30

84

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Stalks of Plane Conic $C \cong \mathbb{P}^1$ are UFD

Published on 25 May 2020 - 18:25

83

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Localizations of $k[y,z]/(1-y^2+z^2)$ UFDs

Published on 26 May 2020 - 14:29

67

Views

An example of a local ring of $V$ at $p$ not ufd

Published on 26 May 2020 - 16:34

164

Views

Flat extension of local rings with a specified extension of residue field

Published on 29 May 2020 - 10:28

List Question

Completion of finite local homomorphism.

Existence of system of parameters via prime avoidance

How much information about $R$ is encoded in its local rings OR in its tangent spaces if I know the topology of $\operatorname{Spec}(R)$?

Dual of a module of finite projective dimension

If in a commutative ring $R$ a maximal ideal is nilpotent, then $R$ is local

Equality in proof of Theorem 14.9 from Harris's book

Cancelling the canonical module in tensor products

Does the category of local rings with residue field $F$ have an initial object?

Is $(\mathbb{Z}/2\mathbb{Z})[T,T^{-1}]$ a DVR?

Prove: $R$ is local $\iff$ $R$ has exactly one maximal ideal.

$R$ be local and suppose $x ∈ R$ satisfies $x^2 = x$

Stalks of Plane Conic $C \cong \mathbb{P}^1$ are UFD

Localizations of $k[y,z]/(1-y^2+z^2)$ UFDs

An example of a local ring of $V$ at $p$ not ufd

Flat extension of local rings with a specified extension of residue field

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