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- Absolute_value_(algebra) abstract "This article is about the generalization of the basic concept. For the basic concept, see Absolute value. For other uses, see Absolute value (disambiguation).In mathematics, an absolute value is a function which measures the \"size\" of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping | x | from D to the real numbers R satisfying: | x | ≥ 0, | x | = 0 if and only if x = 0, | xy | = | x || y |, | x + y | ≤ | x | + | y |.It follows from these axioms that | 1 | = 1 and | −1 | = 1. Furthermore, for every positive integer n,| n | = | 1 + 1 + ...(n times) | = | −1 − 1 − ...(n times) | ≤ n.Note that some authors use the terms valuation, norm, or magnitude instead of \"absolute value\". However, the word \"norm\" usually refers to a specific kind of absolute value on a field (and which is also applied to other vector spaces).The classical \"absolute value\" is one in which, for example, |2|=2. But many other functions fulfill the requirements stated above, for instance the square root of the classical absolute value (but not the square thereof).".
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- Absolute_value_(algebra) wikiPageWikiLink Absolute_value.
- Absolute_value_(algebra) wikiPageWikiLink Absolute_value_(disambiguation).
- Absolute_value_(algebra) wikiPageWikiLink Alexander_Ostrowski.
- Absolute_value_(algebra) wikiPageWikiLink Algebraic_number_theory.
- Absolute_value_(algebra) wikiPageWikiLink Archimedes.
- Absolute_value_(algebra) wikiPageWikiLink Cambridge_University_Press.
- Absolute_value_(algebra) wikiPageWikiLink Category:Abstract_algebra.
- Absolute_value_(algebra) wikiPageWikiLink Cauchy_sequence.
- Absolute_value_(algebra) wikiPageWikiLink Complete_metric_space.
- Absolute_value_(algebra) wikiPageWikiLink Embedding.
- Absolute_value_(algebra) wikiPageWikiLink Field_(mathematics).
- Absolute_value_(algebra) wikiPageWikiLink Field_of_fractions.
- Absolute_value_(algebra) wikiPageWikiLink Function_(mathematics).
- Absolute_value_(algebra) wikiPageWikiLink Integral_domain.
- Absolute_value_(algebra) wikiPageWikiLink Local_ring.
- Absolute_value_(algebra) wikiPageWikiLink Mathematics.
- Absolute_value_(algebra) wikiPageWikiLink Maximal_ideal.
- Absolute_value_(algebra) wikiPageWikiLink Nicolas_Bourbaki.
- Absolute_value_(algebra) wikiPageWikiLink Norm_(mathematics).
- Absolute_value_(algebra) wikiPageWikiLink Ostrowskis_theorem.
- Absolute_value_(algebra) wikiPageWikiLink P-adic_number.
- Absolute_value_(algebra) wikiPageWikiLink Prime_ideal.
- Absolute_value_(algebra) wikiPageWikiLink Quotient_ring.
- Absolute_value_(algebra) wikiPageWikiLink Rational_number.
- Absolute_value_(algebra) wikiPageWikiLink Real_number.
- Absolute_value_(algebra) wikiPageWikiLink Ring_(mathematics).
- Absolute_value_(algebra) wikiPageWikiLink Ultrametric_space.
- Absolute_value_(algebra) wikiPageWikiLink Valuation_(algebra).
- Absolute_value_(algebra) wikiPageWikiLink Valuation_ring.
- Absolute_value_(algebra) wikiPageWikiLinkText "''Archimedean'' absolute value".
- Absolute_value_(algebra) wikiPageWikiLinkText "(Archimedean) absolute value".
- Absolute_value_(algebra) wikiPageWikiLinkText "Absolute value (algebra)".
- Absolute_value_(algebra) wikiPageWikiLinkText "Absolute value (algebra)#Places".
- Absolute_value_(algebra) wikiPageWikiLinkText "Absolute value (algebra)#Types of absolute value".
- Absolute_value_(algebra) wikiPageWikiLinkText "Archimedean absolute value".
- Absolute_value_(algebra) wikiPageWikiLinkText "absolute value (algebra)".
- Absolute_value_(algebra) wikiPageWikiLinkText "absolute value".
- Absolute_value_(algebra) wikiPageWikiLinkText "absolute values".
- Absolute_value_(algebra) wikiPageWikiLinkText "absolute values, valuations, places".
- Absolute_value_(algebra) wikiPageWikiLinkText "archimedean absolute value".
- Absolute_value_(algebra) wikiPageWikiLinkText "non-Archimedean absolute value".
- Absolute_value_(algebra) wikiPageWikiLinkText "trivial absolute value".
- Absolute_value_(algebra) wikiPageWikiLinkText "valued field".
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- Absolute_value_(algebra) wikiPageUsesTemplate Template:Refend.
- Absolute_value_(algebra) wikiPageUsesTemplate Template:Reflist.
- Absolute_value_(algebra) subject Category:Abstract_algebra.
- Absolute_value_(algebra) type Redirect.
- Absolute_value_(algebra) comment "This article is about the generalization of the basic concept. For the basic concept, see Absolute value. For other uses, see Absolute value (disambiguation).In mathematics, an absolute value is a function which measures the \"size\" of elements in a field or integral domain.".
- Absolute_value_(algebra) label "Absolute value (algebra)".
- Absolute_value_(algebra) sameAs Q4669840.
- Absolute_value_(algebra) sameAs Valeur_absolue_ultramétrique.
- Absolute_value_(algebra) sameAs 절댓값_(대수학).
- Absolute_value_(algebra) sameAs Valor_absoluto_(álgebra).
- Absolute_value_(algebra) sameAs m.0d05c2.
- Absolute_value_(algebra) sameAs Нормирование.
- Absolute_value_(algebra) sameAs Q4669840.
- Absolute_value_(algebra) sameAs 绝对赋值.
- Absolute_value_(algebra) wasDerivedFrom Absolute_value_(algebra)?oldid=676258736.
- Absolute_value_(algebra) isPrimaryTopicOf Absolute_value_(algebra).