| dbo:abstract |
In ring theory, a branch of mathematics, a radical of a ring is an ideal of "not-good" elements of the ring. The first example of a radical was the nilradical introduced by , based on a suggestion of . In the next few years several other radicals were discovered, of which the most important example is the Jacobson radical. The general theory of radicals was defined independently by (Amitsur , , ) and . (en) 環論という数学の分野において、環の根基 (radical of a ring) は環の「悪い」元からなるイデアルである。 根基の最初の例は冪零根基であった。これは のサジェスチョンに基づいて、 で導入された。次の数年間でいくつかの他の根基が発見された。それらのうち最も重要な例はジャコブソン根基である。根基の一般論は (Amitsur , , ) と によって独立に定義された。 (ja) Na teoria dos anéis, um ramo da matemática, o radical de um anel é um ideal de elementos "não bons" do anel. O primeiro exemplo de radical foi o introduzido por Köthe (1930), baseado na sugestão de Wedderburn (1908). Nos anos seguintes, vários outros radicais foram descobertos, dos quais o exemplo mais importante é o . A teoria geral dos radicais foi definida independentemente por (Amitsur 1952 , 1954 , 1954b ) e (1953). (pt) |
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| dbo:wikiPageWikiLink |
dbr:Prime_ideal dbr:Queen's_University_at_Kingston dbr:Primitive_ideal dbr:Non-commutative_ring dbr:Bilinear_form dbc:Ideals_(ring_theory) dbr:Rng_(algebra) dbr:Jacobson_radical dbr:Jacobson_ring dbc:Ring_theory dbr:Commutative dbr:Mathematics dbr:Mathematische_Zeitschrift dbr:Nil_ideal dbr:Nilradical_of_a_ring dbr:Noetherian_ring dbr:Nilpotent dbr:Annihilator_(ring_theory) dbr:Ideal_(ring_theory) dbr:Matrix_ring dbr:Maximal_ideal dbr:Division_algebra dbr:Addison-Wesley dbr:Algebra_over_a_ring dbr:Banach_algebra dbr:Hirsch–Plotkin_radical dbr:Marcel_Dekker dbr:Radical_of_a_module dbr:Radical_of_an_ideal dbr:Ring_(mathematics) dbr:Ring_theory dbr:Von_Neumann_regular_ring dbr:Group_(mathematics) dbr:Artinian_module dbr:Zero_ideal dbr:Associative dbr:Set_theory dbr:University_of_Toronto_Press dbr:Image_(mathematics) dbr:Singular_submodule dbr:Finitely_generated_algebra dbr:Simple_ring dbr:Simple_module dbr:Ring_homomorphism dbr:Preimage dbr:Köthe's_conjecture dbr:Springer-Verlag dbr:Kaplansky_radical dbr:Essential_submodule dbr:Semiprime_ideal |
| dbp:first |
V.A. (en) |
| dbp:id |
r/r077130 (en) |
| dbp:last |
Amitsur (en) Andrunakievich (en) |
| dbp:title |
Radical of ring and algebras (en) |
| dbp:wikiPageUsesTemplate |
dbt:Citation dbt:Cn dbt:Harvtxt dbt:Main dbt:Short_description dbt:Harvs dbt:Eom |
| dbp:year |
1952 (xsd:integer) 1954 (xsd:integer) |
| dcterms:subject |
dbc:Ideals_(ring_theory) dbc:Ring_theory |
| gold:hypernym |
dbr:Ideal |
| rdf:type |
yago:Abstraction100002137 yago:Cognition100023271 yago:Content105809192 yago:Idea105833840 yago:Ideal105923696 yago:PsychologicalFeature100023100 yago:WikicatIdeals |
| rdfs:comment |
In ring theory, a branch of mathematics, a radical of a ring is an ideal of "not-good" elements of the ring. The first example of a radical was the nilradical introduced by , based on a suggestion of . In the next few years several other radicals were discovered, of which the most important example is the Jacobson radical. The general theory of radicals was defined independently by (Amitsur , , ) and . (en) 環論という数学の分野において、環の根基 (radical of a ring) は環の「悪い」元からなるイデアルである。 根基の最初の例は冪零根基であった。これは のサジェスチョンに基づいて、 で導入された。次の数年間でいくつかの他の根基が発見された。それらのうち最も重要な例はジャコブソン根基である。根基の一般論は (Amitsur , , ) と によって独立に定義された。 (ja) Na teoria dos anéis, um ramo da matemática, o radical de um anel é um ideal de elementos "não bons" do anel. O primeiro exemplo de radical foi o introduzido por Köthe (1930), baseado na sugestão de Wedderburn (1908). Nos anos seguintes, vários outros radicais foram descobertos, dos quais o exemplo mais importante é o . A teoria geral dos radicais foi definida independentemente por (Amitsur 1952 , 1954 , 1954b ) e (1953). (pt) |
| rdfs:label |
環の根基 (ja) Radical of a ring (en) Radical de um anel (pt) |
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freebase:Radical of a ring yago-res:Radical of a ring wikidata:Radical of a ring dbpedia-he:Radical of a ring dbpedia-ja:Radical of a ring dbpedia-pt:Radical of a ring https://global.dbpedia.org/id/4tNQb |
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