List questions from local-rings

Published on 25 Mar 2026 - 7:43

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Local ring if and only if $x$ or $1-x$ is unit

Published on 16 Apr 2026 - 22:30

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Intersections of Local Rings

Published on 30 Apr 2026 - 14:56

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The vanishing ideal of the complex torus

Published on 12 Apr 2026 - 17:37

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Surjective homomorphism from a faithfully flat module to a regular local ring.

Published on 10 May 2026 - 13:48

73

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What is meant by $\operatorname{Tor}(P,K)$ for $P$ a left $R$-module?

Published on 15 Apr 2026 - 5:03

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Dimension of $m/m^2$ over $k$ where $m=m_P(V)$ and $V=V(x^2-y^3,y^2-z^3)$

Published on 17 Apr 2026 - 2:43

212

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In a commutative local Noetherian ring $R$ with maximal ideal $J$, if $J$ is not nilpotent then $R$ is an integral domain.

Published on 12 Apr 2026 - 21:13

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What possible characteristics may a local commutative unital ring have?

Published on 12 Apr 2026 - 8:43

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Invertible elements in a discrete valuation ring

Published on 17 Apr 2026 - 4:10

36

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Proving that $\mathbb{F}_p[x_1,\dots,x_n]/(x_1^p,\dots,x_n^p)$ is a complete intersection ring

Published on 10 May 2026 - 14:49

44

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A sufficient condition for a unitary ring to be a local ring

Published on 13 Apr 2026 - 19:58

65

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How does Matlis duality behave w.r.t. Hopfian and Co-hopfian modules?

Published on 14 Apr 2026 - 19:55

1k

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Why is $F[x]/(x^n)$ a local ring?

Published on 16 Apr 2026 - 12:33

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Every Artinian ring is isomorphic to a direct product of Artinian local rings

Published on 10 May 2026 - 15:47

List Question

Commutative ring satisfying a.c.c. and d.c.c. on radical ideals

Local ring if and only if $x$ or $1-x$ is unit

Intersections of Local Rings

The vanishing ideal of the complex torus

Surjective homomorphism from a faithfully flat module to a regular local ring.

What is meant by $\operatorname{Tor}(P,K)$ for $P$ a left $R$-module?

Dimension of $m/m^2$ over $k$ where $m=m_P(V)$ and $V=V(x^2-y^3,y^2-z^3)$

In a commutative local Noetherian ring $R$ with maximal ideal $J$, if $J$ is not nilpotent then $R$ is an integral domain.

What possible characteristics may a local commutative unital ring have?

Invertible elements in a discrete valuation ring

Proving that $\mathbb{F}_p[x_1,\dots,x_n]/(x_1^p,\dots,x_n^p)$ is a complete intersection ring

A sufficient condition for a unitary ring to be a local ring

How does Matlis duality behave w.r.t. Hopfian and Co-hopfian modules?

Why is $F[x]/(x^n)$ a local ring?

Every Artinian ring is isomorphic to a direct product of Artinian local rings

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