Matches in SemOpenAlex for { <https://semopenalex.org/work/W87022399> ?p ?o ?g. }
Showing items 1 to 58 of
58
with 100 items per page.
- W87022399 endingPage "11" @default.
- W87022399 startingPage "1" @default.
- W87022399 abstract "A valued field is a field k provided with a valuation (or absolute value). The latter is a map a ↦ |a| from k to R which satisfies the rules: $$ begin{gathered} 1. left| a right| geqslant 0 and left| a right| = 0 if and only if a = 0. hfill 2. left| {ab} right| = left| a right| cdot left| b right|. hfill 3. left| {a + b} right| leqslant left| a right| + left| b right|. hfill end{gathered} $$ The absolute values on the fields R and C make these fields into valued fields. In the present context the most important valued fields are the so-called nonarchimedean valued fields. They are defined by replacing the triangle inequality $$ left| {a + b} right| leqslant left| a right| + left| b right| $$ with the stronger inequality $$ left| {a + b} right| leqslant max left( {left| a right|,left| b right|} right) $$ . The trivial valuation is defined by $$ left| 0 right| = 0 and left| a right| = 1 for a in k^* $$ . In what follows we will mean by valuation and valued field, a non-trivial, non-archimedean valuation and a field equipped with such a valuation." @default.
- W87022399 created "2016-06-24" @default.
- W87022399 creator A5007957077 @default.
- W87022399 creator A5030913253 @default.
- W87022399 date "2004-01-01" @default.
- W87022399 modified "2023-09-25" @default.
- W87022399 title "Valued Fields and Normed Spaces" @default.
- W87022399 doi "https://doi.org/10.1007/978-1-4612-0041-3_1" @default.
- W87022399 hasPublicationYear "2004" @default.
- W87022399 type Work @default.
- W87022399 sameAs 87022399 @default.
- W87022399 citedByCount "0" @default.
- W87022399 crossrefType "book-chapter" @default.
- W87022399 hasAuthorship W87022399A5007957077 @default.
- W87022399 hasAuthorship W87022399A5030913253 @default.
- W87022399 hasConcept C10138342 @default.
- W87022399 hasConcept C127413603 @default.
- W87022399 hasConcept C144133560 @default.
- W87022399 hasConcept C166957645 @default.
- W87022399 hasConcept C186027771 @default.
- W87022399 hasConcept C202444582 @default.
- W87022399 hasConcept C205649164 @default.
- W87022399 hasConcept C2776719672 @default.
- W87022399 hasConcept C2779343474 @default.
- W87022399 hasConcept C33923547 @default.
- W87022399 hasConcept C66938386 @default.
- W87022399 hasConcept C9652623 @default.
- W87022399 hasConceptScore W87022399C10138342 @default.
- W87022399 hasConceptScore W87022399C127413603 @default.
- W87022399 hasConceptScore W87022399C144133560 @default.
- W87022399 hasConceptScore W87022399C166957645 @default.
- W87022399 hasConceptScore W87022399C186027771 @default.
- W87022399 hasConceptScore W87022399C202444582 @default.
- W87022399 hasConceptScore W87022399C205649164 @default.
- W87022399 hasConceptScore W87022399C2776719672 @default.
- W87022399 hasConceptScore W87022399C2779343474 @default.
- W87022399 hasConceptScore W87022399C33923547 @default.
- W87022399 hasConceptScore W87022399C66938386 @default.
- W87022399 hasConceptScore W87022399C9652623 @default.
- W87022399 hasLocation W870223991 @default.
- W87022399 hasOpenAccess W87022399 @default.
- W87022399 hasPrimaryLocation W870223991 @default.
- W87022399 hasRelatedWork W1974190782 @default.
- W87022399 hasRelatedWork W2032183060 @default.
- W87022399 hasRelatedWork W2097957663 @default.
- W87022399 hasRelatedWork W2112111778 @default.
- W87022399 hasRelatedWork W2332203959 @default.
- W87022399 hasRelatedWork W2348631976 @default.
- W87022399 hasRelatedWork W2368290924 @default.
- W87022399 hasRelatedWork W2980233689 @default.
- W87022399 hasRelatedWork W4233516208 @default.
- W87022399 hasRelatedWork W4254014287 @default.
- W87022399 isParatext "false" @default.
- W87022399 isRetracted "false" @default.
- W87022399 magId "87022399" @default.
- W87022399 workType "book-chapter" @default.