About: Torsionless module

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In abstract algebra, a module M over a ring R is called torsionless if it can be embedded into some direct product RI. Equivalently, M is torsionless if each non-zero element of M has non-zero image under some R-linear functional f: This notion was introduced by Hyman Bass.

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rdf:type	Thing yago:Abstraction100002137 yago:Cognition100023271 yago:Explanation105793000 yago:HigherCognitiveProcess105770664 yago:Process105701363 yago:PsychologicalFeature100023100 yago:Theory105989479 yago:Thinking105770926 yago:WikicatDualityTheories
rdfs:label	不ねじれ加群 (ja) 반사 가군 (ko) Torsionless module (en)
rdfs:comment	In abstract algebra, a module M over a ring R is called torsionless if it can be embedded into some direct product RI. Equivalently, M is torsionless if each non-zero element of M has non-zero image under some R-linear functional f: This notion was introduced by Hyman Bass. (en) 환론에서 반사 가군(反射加群, 영어: reflexive module)은 스스로의 이중 쌍대 가군과 동형인 가군이다. (ko) 不ねじれ加群（ふねじれかぐん　英: torsionless module）とは、代数学における環上の加群について、自身から二重双対加群への正準写像（ χ : M → M** ）が、単射であるような加群 M の事をいう。同値なことだが、台の環を R とおくとき、０M 以外、M の何れの元も、R-線形汎函数によって 0R へと写されることがないような加群 M の事であるともいえる。 (ja)
differentFrom	Torsion-free module
dcterms:subject	Module theory
Wikipage page ID	27481586 (xsd:integer)
Wikipage revision ID	1073758925 (xsd:integer)
Link from a Wikipage to another Wikipage	Module (mathematics) Module theory Hyman Bass Integral domain Prüfer domain Commutative ring Domain (ring theory) Finitely generated module Flat module Direct product Direct sum Projective module Ring (mathematics) Abstract algebra Coherent ring Torsion-free module Free module Semihereditary ring Injective Reflexive sheaf Springer-Verlag Springer Verlag
sameAs	Torsionless module Torsionless module Torsionless module Torsionless module Torsionless module
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Citation_needed dbt:Distinguish dbt:Reflist dbt:Sfn
has abstract	In abstract algebra, a module M over a ring R is called torsionless if it can be embedded into some direct product RI. Equivalently, M is torsionless if each non-zero element of M has non-zero image under some R-linear functional f: This notion was introduced by Hyman Bass. (en) 환론에서 반사 가군(反射加群, 영어: reflexive module)은 스스로의 이중 쌍대 가군과 동형인 가군이다. (ko) 不ねじれ加群（ふねじれかぐん　英: torsionless module）とは、代数学における環上の加群について、自身から二重双対加群への正準写像（ χ : M → M** ）が、単射であるような加群 M の事をいう。同値なことだが、台の環を R とおくとき、０M 以外、M の何れの元も、R-線形汎函数によって 0R へと写されることがないような加群 M の事であるともいえる。 (ja)
prov:wasDerivedFrom	wikipedia-en:Torsionless_module?oldid=1073758925&ns=0
page length (characters) of wiki page	4776 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Torsionless_module
is differentFrom of	Torsion-free module
is Link from a Wikipage to another Wikipage of	Module (mathematics) Prüfer domain Glossary of commutative algebra Glossary of module theory Dual module Torsion-free module Reflexive module Reflexive sheaf
is Wikipage redirect of	Reflexive module
is foaf:primaryTopic of	wikipedia-en:Torsionless_module

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