List questions from valuation-theory

Published on 17 Aug 2022 - 17:18

33

Views

If a DVR in $k(x)$ contains $x$, then its maximal ideal contains some polynomial

Published on 24 Aug 2022 - 16:12

87

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The quotient of totally ordered additive abelian groups which is torsion (value groups in valuation theory)

Published on 23 Feb 2026 - 8:27

109

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Completion of Function Field $K$ isomorphic to $\kappa_A((T))$

Published on 09 Sep 2022 - 23:13

125

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Number of absolute values on fields of characteristic $0$

Published on 21 Sep 2022 - 9:47

224

Views

Is $\mathbb{Z}_p$ the only discrete valuation ring of $\mathbb{Q}_p$

Published on 27 Mar 2026 - 16:54

60

Views

Valuation rings over a field that is algebraic over a finite subfield, are there any?

Published on 29 Sep 2022 - 16:32

104

Views

Can inequivalent Krull valuations induce the same topology?

Published on 23 Feb 2026 - 4:55

139

Views

Extension of p-adic valuation to number field

Published on 18 Oct 2022 - 9:43

141

Views

Normalization of Vector in arbitrary Normed Vector Space

Published on 19 Oct 2022 - 18:40

48

Views

Why for discrete valuation fields $K\subset L$ it holds that $\mathcal O_K \subset \mathcal O_L$?

Published on 27 Mar 2026 - 16:55

47

Views

Proof of sufficient condition for an extension to be unramified

Published on 25 Mar 2026 - 11:32

66

Views

Finiteness of the degree of residue fields of valuation rings

Published on 02 Nov 2022 - 1:46

91

Views

A maximal ring wrt Domination is a valuation ring.

Published on 22 Nov 2022 - 1:52

44

Views

Consequences of definitions in Local fields

Published on 27 Mar 2026 - 0:10

List Question

If two direct sums of modules are isomorphic, when do we know that the components are isomorphic?

If a DVR in $k(x)$ contains $x$, then its maximal ideal contains some polynomial

The quotient of totally ordered additive abelian groups which is torsion (value groups in valuation theory)

Completion of Function Field $K$ isomorphic to $\kappa_A((T))$

Number of absolute values on fields of characteristic $0$

Is $\mathbb{Z}_p$ the only discrete valuation ring of $\mathbb{Q}_p$

Valuation rings over a field that is algebraic over a finite subfield, are there any?

Can inequivalent Krull valuations induce the same topology?

Extension of p-adic valuation to number field

Normalization of Vector in arbitrary Normed Vector Space

Why for discrete valuation fields $K\subset L$ it holds that $\mathcal O_K \subset \mathcal O_L$?

Proof of sufficient condition for an extension to be unramified

Finiteness of the degree of residue fields of valuation rings

A maximal ring wrt Domination is a valuation ring.

Consequences of definitions in Local fields

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