Question

If $f(x) = g(x)h(x)$ and $f(x)$ has non-negative valuation then $g(x)$ and $h(x)$ also have non-negative valuation

score 63 · Answer 1 · 2021-05-04 18:14:26

63

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If $f(x) = g(x)h(x)$ and $f(x)$ has non-negative valuation then $g(x)$ and $h(x)$ also have non-negative valuation

Published on 04 May 2021 - 18:14

score 40 · Answer 2 · 2021-05-13 21:57:11

40

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score 172 · Answer 6 · 2021-05-25 13:09:04

172

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score 179 · Answer 7 · 2026-03-27 07:49:49

179

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score 356 · Answer 8 · 2021-06-20 08:07:54

356

Views

Maximal ideal $\mathfrak m$ of a non-discrete valuation ring of rank one satisfies $\mathfrak{m}^{2}=\mathfrak{m}$

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score 101 · Answer 9 · 2021-06-22 09:48:20

101

Views

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score 123 · Answer 10 · 2026-02-23 08:19:22

123

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479

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score 132 · Answer 12 · 2021-06-29 17:41:52

132

Views

$\mathrm{Spa}(A,A)=\{A\to V \text{ valuation ring}\}$ modulo faithfully flat maps

Published on 29 Jun 2021 - 17:41

score 49 · Answer 13 · 2021-06-29 22:58:18

49

Views

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score 662 · Answer 14 · 2021-06-30 11:22:54

662

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Let $A$ be a valuation ring of a field $K$. Show that every subring of $K$ which contains $A$ is a local ring of $A$.

Published on 30 Jun 2021 - 11:22

score 922 · Answer 15 · 2021-07-03 14:09:45

922

Views

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Published on 03 Jul 2021 - 14:09

List Question

If $f(x) = g(x)h(x)$ and $f(x)$ has non-negative valuation then $g(x)$ and $h(x)$ also have non-negative valuation

Recommend text on non-singular plane curves and DVRs

Show the existence of a valuation with a given residue field

Some questions about absolute value on number fields.

Are there any useful generalizations of homomorphisms that can apply to a graded valuation ring?

Two meanings of "residue field"

Vanishing order of a modular form at an irregular cusp: why is it treated like a valuation?

Maximal ideal $\mathfrak m$ of a non-discrete valuation ring of rank one satisfies $\mathfrak{m}^{2}=\mathfrak{m}$

Element where all valuations are zero

The composite valuation

Number of rank-one valuation rings

$\mathrm{Spa}(A,A)=\{A\to V \text{ valuation ring}\}$ modulo faithfully flat maps

Generalizing valuations

Let $A$ be a valuation ring of a field $K$. Show that every subring of $K$ which contains $A$ is a local ring of $A$.

Module $M$ over valuation Ring $A$ is flat $\iff$ it is torsion free

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