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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  • 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)
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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. (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)
rdfs:label
  • 不ねじれ加群 (ja)
  • 반사 가군 (ko)
  • Torsionless module (en)
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