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15
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Showing degree of global extension is sum of degree of local extensions

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#abstract-algebra #field-theory #algebraic-number-theory #valuation-theory #local-field
45
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Valuation ring $(A,\mathfrak{m})$ so that $\text{Spec }A\setminus\{\mathfrak{m}\}$ has no closed points

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#commutative-algebra #valuation-theory
37
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Prolongation valuation of non-complete valued field

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#abstract-algebra #galois-theory #extension-field #valuation-theory #local-rings
67
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Non-isomorphic models of Hen$_{0,0}$ with isomorphic RV sorts

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#logic #model-theory #valuation-theory
46
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Valuation rings come from valuation functions

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#abstract-algebra #valuation-theory
82
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Value group of the $p$-adic complex numbers

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#number-theory #algebraic-number-theory #p-adic-number-theory #valuation-theory
33
Views

Can we define valuation(s) in any integral ring?

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#number-theory #ring-theory #ideals #maximal-and-prime-ideals #valuation-theory
51
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How to express elements of a DVR as power series of the uniformizer?

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#algebraic-geometry #commutative-algebra #valuation-theory #local-rings
97
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Why do we fix an extension of valuation of $K$ to $\overline{K}$?

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#abstract-algebra #field-theory #notation #algebraic-number-theory #valuation-theory
28
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What's a direct or quickest proof of simple zeros lift to factorizations lift?

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#field-theory #valuation-theory #hensels-lemma
71
Views

Is the dimension of a valuation ring equal to the rank of its value group?

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#commutative-algebra #valuation-theory
19
Views

Why is this proof of an inequality in a DVR valid?

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#abstract-algebra #inequality #valuation-theory
48
Views

Analytic equivalence and isomorphism of valued fields

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#commutative-algebra #field-theory #algebraic-number-theory #extension-field #valuation-theory
90
Views

Valuation on $K(x, y)$ similar to $\mathfrak{p}$-adic valuation

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#commutative-algebra #algebraic-number-theory #extension-field #valuation-theory #krull-dimension
109
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A case where submodules, isomorphic as modules, are isomorphic as submodules

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#commutative-algebra #principal-ideal-domains #valuation-theory #artinian

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