List questions from dimension-theory-algebra

398

Views

How to prove that $\dim \mathrm{Spec}~A = \dim \mathrm{Spec}~ A_\mathfrak{p} + \dim \mathrm{Spec}~A/\mathfrak{p}$.

Published on 22 Mar 2026 - 19:39

345

Views

Proof of Krull's Height Theorem for irreducible affine varieties

Published on 23 Mar 2026 - 4:34

159

Views

Connected components of an open subset

Published on 22 Mar 2026 - 9:51

137

Views

Valuation ring of finite Krull dimension whose every non-maximal ideal is principal

Published on 17 Mar 2026 - 1:53

690

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What are the discrete valuation rings for the affine plane?

Published on 16 Mar 2026 - 22:21

453

Views

Extending a morphism to a projective scheme

Published on 22 Mar 2026 - 18:11

1.6k

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Proof of Theorem of Dimension of Fibres

Published on 22 Mar 2026 - 16:00

58

Views

How to define $\operatorname{dim}(\{0\})$ and $\operatorname{ht}(A)$?

Published on 17 Mar 2026 - 14:53

371

Views

Exercise 1.8 from Hartshorne

Published on 22 Mar 2026 - 8:01

209

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Dimension of a hypersurface of $\mathbb C^n$ / of a cut by a hypersurface

Published on 17 Mar 2026 - 11:06

66

Views

Axioms that characterize the notion of dimension

Published on 17 Mar 2026 - 15:37

45

Views

Does $\operatorname{length}(M/xM) \leq \operatorname{rank}(M) \cdot \operatorname{length}(R/(x))$ hold over non-integral rings $R$?

Published on 17 Mar 2026 - 9:18

187

Views

Infinite Noetherian ring of dimension $1$ in which distinct non-zero ideals have distinct and finite index

Published on 23 Mar 2026 - 20:03

225

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a.c.c. and d.c.c. on radical ideals in commutative ring of dimension zero

Published on 17 Mar 2026 - 0:34

64

Views

Dimension of affine affine algebras as a module

Published on 22 Mar 2026 - 17:36

List Question

How to prove that $\dim \mathrm{Spec}~A = \dim \mathrm{Spec}~ A_\mathfrak{p} + \dim \mathrm{Spec}~A/\mathfrak{p}$.

Proof of Krull's Height Theorem for irreducible affine varieties

Connected components of an open subset

Valuation ring of finite Krull dimension whose every non-maximal ideal is principal

What are the discrete valuation rings for the affine plane?

Extending a morphism to a projective scheme

Proof of Theorem of Dimension of Fibres

How to define $\operatorname{dim}(\{0\})$ and $\operatorname{ht}(A)$?

Exercise 1.8 from Hartshorne

Dimension of a hypersurface of $\mathbb C^n$ / of a cut by a hypersurface

Axioms that characterize the notion of dimension

Does $\operatorname{length}(M/xM) \leq \operatorname{rank}(M) \cdot \operatorname{length}(R/(x))$ hold over non-integral rings $R$?

Infinite Noetherian ring of dimension $1$ in which distinct non-zero ideals have distinct and finite index

a.c.c. and d.c.c. on radical ideals in commutative ring of dimension zero

Dimension of affine affine algebras as a module

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