List questions from dimension-theory-algebra

Published on 25 Mar 2026 - 17:45

240

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Is the dimension of a Noetherian local ring equal to its associated graded ring?

Published on 25 Mar 2026 - 17:39

383

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Exercise 11.1.G Vakil FOAG

Published on 25 Mar 2026 - 17:38

347

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Proof of Proposition 11.20 of Atiyah-Macdonald

Published on 25 Mar 2026 - 23:39

363

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Proof of Hilbert-Serre [Atiyah-Macdonald thm 11.1]

Published on 25 Mar 2026 - 17:39

71

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If $I\subset S$ is the homogeneous ideal of a finite set of points in $\mathbb P^n$, then $\dim S/I=1$.

Published on 25 Mar 2026 - 17:41

64

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A set with co-dimension less continuum

Published on 25 Mar 2026 - 20:41

35

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What is the dimension of $\mathbb{C}[X,Y,Z] / \langle X^{c-2} , Y^c , Z^c \rangle$ as a vector space over $\mathbb{C}$?

Published on 25 Mar 2026 - 19:10

74

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Does the notion of projective/injective dimension exist for chain complexes?

Published on 25 Mar 2026 - 17:45

599

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What is the "dimension" of a locally ringed space?

Published on 09 Apr 2026 - 17:48

727

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How many times harder is to think in 3D as compared with 2D?

Published on 25 Mar 2026 - 17:39

80

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For $0 \xrightarrow{f_0} \mathbb{C}^n \xrightarrow{f_1} \mathbb{C}^\ell \xrightarrow{f_2} \mathbb{C}^r \xrightarrow{f_3} 0$, what is $\ell$?

Published on 25 Mar 2026 - 17:44

911

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Does the number of elements in Vector space and the dimension of Vector space same?

Published on 25 Mar 2026 - 19:03

108

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Fibered product of varieties and dimension

Published on 15 Apr 2026 - 12:05

84

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Dimension counting in exact sequences of Hopf algebras

Published on 25 Mar 2026 - 19:05

List Question

Proving second injective change of rings theorem

Is the dimension of a Noetherian local ring equal to its associated graded ring?

Exercise 11.1.G Vakil FOAG

Proof of Proposition 11.20 of Atiyah-Macdonald

Proof of Hilbert-Serre [Atiyah-Macdonald thm 11.1]

If $I\subset S$ is the homogeneous ideal of a finite set of points in $\mathbb P^n$, then $\dim S/I=1$.

A set with co-dimension less continuum

What is the dimension of $\mathbb{C}[X,Y,Z] / \langle X^{c-2} , Y^c , Z^c \rangle$ as a vector space over $\mathbb{C}$?

Does the notion of projective/injective dimension exist for chain complexes?

What is the "dimension" of a locally ringed space?

How many times harder is to think in 3D as compared with 2D?

For $0 \xrightarrow{f_0} \mathbb{C}^n \xrightarrow{f_1} \mathbb{C}^\ell \xrightarrow{f_2} \mathbb{C}^r \xrightarrow{f_3} 0$, what is $\ell$?

Does the number of elements in Vector space and the dimension of Vector space same?

Fibered product of varieties and dimension

Dimension counting in exact sequences of Hopf algebras

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