About: Primitive ring

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In the branch of abstract algebra known as ring theory, a left primitive ring is a ring which has a faithful simple left module. Well known examples include endomorphism rings of vector spaces and Weyl algebras over fields of characteristic zero.

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rdfs:label	원시환 (ko) 原始環 (ja) Primitive ring (en) Anel primitivo (pt)
rdfs:comment	In the branch of abstract algebra known as ring theory, a left primitive ring is a ring which has a faithful simple left module. Well known examples include endomorphism rings of vector spaces and Weyl algebras over fields of characteristic zero. (en) 環論において、左原始環（ひだりげんしかん、英: left primitive ring）とは、忠実な単純左加群をもつ環である。よく知られた例として、ベクトル空間の自己準同型環や、標数0の体上のワイル代数がある。 (ja) 환론에서 원시환(原始環, 영어: primitive ring)은 단순 가군으로서 완전히 나타낼 수 있는 환이다. 이러한 환들은 나눗셈환 위의 선형 변환들의 환에 가깝다. (ko) Na subárea da álgebra abstrata conhecida como teoria de anéis, um anel primitivo à esquerda é um anel que possui um módulo à esquerda fiel simples. Entre os exemplos bem conhecidos estão os de espaços vetoriais sobre corpos de característica zero. (pt)
dcterms:subject	Ring theory Algebraic structures
Wikipage page ID	485862 (xsd:integer)
Wikipage revision ID	1096045022 (xsd:integer)
Link from a Wikipage to another Wikipage	Product ring Endomorphism ring Module (mathematics) Prime ring Primitive ideal Vector spaces Injective module Ring theory George Bergman Subring Quotient module Morita equivalence Annihilator (ring theory) Linear algebra Commutative ring Ideal (ring theory) Matrix ring Maximal ideal Algebraic structures Weyl algebra Domain (ring theory) Faithful module Field (mathematics) Length of a module Ring (mathematics) Ring theory Jacobson density theorem Abstract algebra Characteristic (algebra) Division ring Artinian ring Socle (mathematics) Semisimple ring Linear transformation Semiprimitive ring Simple ring Simple module Von Neumann regular Ring homomorphism Ring of endomorphisms
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=2T5DAAAAQBAJ&pg=PA191 https://www.jstor.org/stable/2034929
sameAs	Primitive ring Primitive ring Primitive ring Primitive ring Primitive ring Primitive ring Primitive ring Primitive ring
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:Harvtxt dbt:No_footnotes dbt:Reflist dbt:Sfn dbt:Harvnb
has abstract	In the branch of abstract algebra known as ring theory, a left primitive ring is a ring which has a faithful simple left module. Well known examples include endomorphism rings of vector spaces and Weyl algebras over fields of characteristic zero. (en) 環論において、左原始環（ひだりげんしかん、英: left primitive ring）とは、忠実な単純左加群をもつ環である。よく知られた例として、ベクトル空間の自己準同型環や、標数0の体上のワイル代数がある。 (ja) 환론에서 원시환(原始環, 영어: primitive ring)은 단순 가군으로서 완전히 나타낼 수 있는 환이다. 이러한 환들은 나눗셈환 위의 선형 변환들의 환에 가깝다. (ko) Na subárea da álgebra abstrata conhecida como teoria de anéis, um anel primitivo à esquerda é um anel que possui um módulo à esquerda fiel simples. Entre os exemplos bem conhecidos estão os de espaços vetoriais sobre corpos de característica zero. (pt)
gold:hypernym	Ring
prov:wasDerivedFrom	wikipedia-en:Primitive_ring?oldid=1096045022&ns=0
page length (characters) of wiki page	6232 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Primitive_ring
is Link from a Wikipage to another Wikipage of	List of abstract algebra topics Prime ring Primitive ideal Double centralizer theorem Jacobson radical Pseudoelementary class Full linear ring Glossary of ring theory Morita equivalence Noncommutative ring Ring theory Jacobson density theorem Right primitive ring Singular submodule

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