About: Archimedean group

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In abstract algebra, a branch of mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements are bounded by integer multiples of each other. The set R of real numbers together with the operation of addition and the usual ordering relation between pairs of numbers is an Archimedean group. By a result of Otto Hölder, every Archimedean group is isomorphic to a subgroup of this group. The name "Archimedean" comes from Otto Stolz, who named the Archimedean property after its appearance in the works of Archimedes.

Attributes	Values
rdf:type	yago:WikicatOrderedGroups yago:Abstraction100002137 yago:Group100031264
rdfs:label	Archimedean group (en) Grup Archimedean (in)
rdfs:comment	In abstract algebra, a branch of mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements are bounded by integer multiples of each other. The set R of real numbers together with the operation of addition and the usual ordering relation between pairs of numbers is an Archimedean group. By a result of Otto Hölder, every Archimedean group is isomorphic to a subgroup of this group. The name "Archimedean" comes from Otto Stolz, who named the Archimedean property after its appearance in the works of Archimedes. (en) Dalam aljabar abstrak, sebuah cabang dari matematika, Grup Archimedean adalah yang sifat Archimedean berlaku: setiap dua elemen grup positif dibatasi oleh kelipatan bilangan bulat satu sama lain. Himpunan R dari bilangan real bersama dengan operasi penjumlahan dan hubungan urutan biasa antara pasangan bilangan adalah grup Archimedean. Dengan hasil dari Otto Hölder, setiap grup Archimedean menjadi subgrup dari grup ini. Nama "Archimedean" berasal dari , yang menamai properti Archimedean setelah kemunculannya dalam karya Archimedes. (in)
dcterms:subject	Ordered groups
Wikipage page ID	264169 (xsd:integer)
Wikipage revision ID	1123936524 (xsd:integer)
Link from a Wikipage to another Wikipage	Archimedean property Ordered groups Dedekind cut Dyadic rational Commutative monoid Commutative property Mathematics Non-Archimedean ordered field Origin (mathematics) Monoid Converse (logic) Lexicographic order Linear order Embedding Hahn embedding theorem Identity element Otto Stolz Subgroup Surreal number Linearly ordered group Cyclic group Even number Non-standard analysis Otto Hölder P-adic number Mathematical proof Group (mathematics) Inverse element Isomorphic Hyperreal number Archimedes Associativity Abelian group Abstract algebra Binary operation Pointwise Group isomorphism Infinitesimal Integer Natural number Operation (mathematics) Rational number Real number Euclidean plane Finite group Archimedean equivalence Cartesian coordinate
sameAs	Archimedean group Archimedean group Archimedean group Archimedean group Archimedean group
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Short_description
has abstract	In abstract algebra, a branch of mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements are bounded by integer multiples of each other. The set R of real numbers together with the operation of addition and the usual ordering relation between pairs of numbers is an Archimedean group. By a result of Otto Hölder, every Archimedean group is isomorphic to a subgroup of this group. The name "Archimedean" comes from Otto Stolz, who named the Archimedean property after its appearance in the works of Archimedes. (en) Dalam aljabar abstrak, sebuah cabang dari matematika, Grup Archimedean adalah yang sifat Archimedean berlaku: setiap dua elemen grup positif dibatasi oleh kelipatan bilangan bulat satu sama lain. Himpunan R dari bilangan real bersama dengan operasi penjumlahan dan hubungan urutan biasa antara pasangan bilangan adalah grup Archimedean. Dengan hasil dari Otto Hölder, setiap grup Archimedean menjadi subgrup dari grup ini. Nama "Archimedean" berasal dari , yang menamai properti Archimedean setelah kemunculannya dalam karya Archimedes. (in)
prov:wasDerivedFrom	wikipedia-en:Archimedean_group?oldid=1123936524&ns=0
page length (characters) of wiki page	9920 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Archimedean_group
is Link from a Wikipage to another Wikipage of	Partially ordered ring Algebraic structure Archimedean property Valuation (algebra) Construction of the real numbers Hahn embedding theorem List of things named after Archimedes Linearly ordered group Cyclically ordered group Archimedean monoid Archimedean Tarski's axiomatization of the reals
is Wikipage redirect of	Archimedean monoid
is Wikipage disambiguates of	Archimedean
is foaf:primaryTopic of	wikipedia-en:Archimedean_group

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