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Do all global fields have infinitely many principal prime ideals?

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#algebraic-number-theory #valuation-theory #local-field
178
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Does analytic completion commute with norm/valuation?

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#real-analysis #abstract-algebra #field-theory #valuation-theory
62
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Completeness and model completeness of the first order theory of Valuation rings

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#logic #commutative-algebra #first-order-logic #model-theory #valuation-theory
43
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Ideals associated to valuations

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#commutative-algebra #valuation-theory
191
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Theorem 11.2 in Matsumura

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#commutative-algebra #valuation-theory
109
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If every proper overring of $R$ is a valuation domain, then $R$ is a valuation domain?

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#abstract-algebra #ring-theory #commutative-algebra #integral-domain #valuation-theory
922
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Prime ideal in valuation ring

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#maximal-and-prime-ideals #valuation-theory
372
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comparison between valuation ring and proper morphism

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#algebraic-geometry #ring-theory #valuation-theory
481
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Valuations and different ideal in local fields

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#algebraic-number-theory #valuation-theory #local-field
49
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Different of an element references

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#reference-request #commutative-algebra #algebraic-number-theory #valuation-theory #local-field
106
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Criterion of separatedness and propernesss

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#algebraic-geometry #commutative-algebra #valuation-theory
55
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Absolute value of the difference is sufficiently small implies the quotient is close to 1

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#algebraic-number-theory #valuation-theory #local-field
89
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Proof of valuation property (function on $K(X_1,\,\dots,\, X_n)$)

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#abstract-algebra #valuation-theory #multivariate-polynomial
139
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Valuation ring whose unique maximal ideal and every ideal of finite height is principal

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#commutative-algebra #maximal-and-prime-ideals #valuation-theory #krull-dimension #local-rings
144
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Valuation ring of finite Krull dimension whose every non-maximal ideal is principal

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#commutative-algebra #valuation-theory #krull-dimension #local-rings #dimension-theory-algebra

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