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- Jacobson_radical abstract "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 (Jacobson 1945).The Jacobson radical of a ring has numerous internal characterizations, including a few definitions that successfully extend the notion to rings without unity. The radical of a module extends the definition of the Jacobson radical to include modules. The Jacobson radical plays a prominent role in many ring and module theoretic results, such as Nakayama's lemma.".
- Jacobson_radical wikiPageID "57656".
- Jacobson_radical wikiPageRevisionID "603393117".
- Jacobson_radical hasPhotoCollection Jacobson_radical.
- Jacobson_radical subject Category:Ideals.
- Jacobson_radical subject Category:Ring_theory.
- Jacobson_radical type Abstraction100002137.
- Jacobson_radical type Cognition100023271.
- Jacobson_radical type Content105809192.
- Jacobson_radical type Idea105833840.
- Jacobson_radical type Ideal105923696.
- Jacobson_radical type Ideals.
- Jacobson_radical type PsychologicalFeature100023100.
- Jacobson_radical comment "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.".
- Jacobson_radical label "Jacobson radical".
- Jacobson_radical label "Jacobson-Radikal".
- Jacobson_radical label "Jacobson-radicaal".
- Jacobson_radical label "Radical de Jacobson".
- Jacobson_radical label "Radicale di Jacobson".
- Jacobson_radical label "Radykał Jacobsona".
- Jacobson_radical label "Радикал Джекобсона".
- Jacobson_radical label "雅各布森根".
- Jacobson_radical sameAs Jacobson-Radikal.
- Jacobson_radical sameAs Radical_de_Jacobson.
- Jacobson_radical sameAs Radicale_di_Jacobson.
- Jacobson_radical sameAs Jacobson-radicaal.
- Jacobson_radical sameAs Radykał_Jacobsona.
- Jacobson_radical sameAs m.0ftmd.
- Jacobson_radical sameAs Q1677769.
- Jacobson_radical sameAs Q1677769.
- Jacobson_radical sameAs Jacobson_radical.
- Jacobson_radical wasDerivedFrom Jacobson_radical?oldid=603393117.
- Jacobson_radical isPrimaryTopicOf Jacobson_radical.