Jacobson radical
In mathematics, more specifically ring theory, a branch of abstract algebra, the Jacobson radical of a ring R is the ideal consisting of those elements in R that annihilate all simple right R-modules. It happens that substituting "left" in place of "right" in the definition yields the same ideal, and so the notion is left-right symmetric. The Jacobson radical of a ring is frequently denoted by J(R) or rad(R); however to avoid confusion with other radicals of rings, the former notation will be preferred in this article. The Jacobson radical is named after Nathan Jacobson, who was the first to study it for arbitrary rings in ().
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Jacobson radical
In mathematics, more specifically ring theory, a branch of abstract algebra, the Jacobson radical of a ring R is the ideal consisting of those elements in R that annihilate all simple right R-modules. It happens that substituting "left" in place of "right" in the definition yields the same ideal, and so the notion is left-right symmetric. The Jacobson radical of a ring is frequently denoted by J(R) or rad(R); however to avoid confusion with other radicals of rings, the former notation will be preferred in this article. The Jacobson radical is named after Nathan Jacobson, who was the first to study it for arbitrary rings in ().
has abstract
En algèbre, le radical de Jaco ...... les idéaux maximaux à droite.
@fr
In de abstracte algebra, meer ...... Jacobson-radicaal bestudeerde.
@nl
In der Ringtheorie, einem Zwei ...... es als erster untersucht hat.
@de
In matematica, il radicale di ...... re ambiguità con il radicale).
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In mathematics, more specifica ...... lts, such as Nakayama's lemma.
@en
Radykał Jacobsona – ideał obus ...... roku przez Nathana Jacobsona.
@pl
Радикалом Джекобсона кольца на ...... она совпадает с нильрадикалом.
@ru
在抽象代数之分支环理论中，一个环 R 的雅各布森根（Jacobson radical）是 R 的一个理想，包含在某种意义上“与零接近”的那些元素。
@zh
数学、より詳しくは抽象代数学の一分野である環論において、環 ...... 理論の結果、例えば中山の補題において、際立った役割を果たす。
@ja
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En algèbre, le radical de Jaco ...... appartient à un idéal maximal.
@fr
In de abstracte algebra, meer ...... ordt vaak aangeduid met J( R).
@nl
In der Ringtheorie, einem Zwei ...... es als erster untersucht hat.
@de
In matematica, il radicale di ...... per anelli arbitrari nel 1945.
@it
In mathematics, more specifica ...... it for arbitrary rings in ().
@en
Radykał Jacobsona – ideał obus ...... roku przez Nathana Jacobsona.
@pl
Радикалом Джекобсона кольца на ...... она совпадает с нильрадикалом.
@ru
在抽象代数之分支环理论中，一个环 R 的雅各布森根（Jacobson radical）是 R 的一个理想，包含在某种意义上“与零接近”的那些元素。
@zh
数学、より詳しくは抽象代数学の一分野である環論において、環 ...... 理論の結果、例えば中山の補題において、際立った役割を果たす。
@ja
label
Jacobson radical
@en
Jacobson-Radikal
@de
Jacobson-radicaal
@nl
Radical de Jacobson
@fr
Radicale di Jacobson
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Radykał Jacobsona
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Радикал Джекобсона
@ru
ジャコブソン根基
@ja
雅各布森根
@zh