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 (Jacobson 1945).

单词	Radical ring
释义	Radical ring 英语百科 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 (Jacobson 1945).
随便看	ferroelasicity的意思 ferroelastic的意思 ferroelastic crystal的意思 ferroelastic domain的意思 ferroelastic effect的意思 ferroelasticity的意思 ferroelastic phase transformation的意思 ferroelastic phase transition的意思 ferroelastics的意思 ferroelctric shift register的意思 ferroelecricity的意思 ferroelecteicity的意思 ferroelectric的意思 ferroelectrically的意思 ferroelectric amplifier的意思 ferroelectric array的意思 ferroelectric autostabilization effect的意思 ferroelectric axis的意思 Ferroelectric capacitor的意思 ferroelectric, capacitor的意思 ferroelectric capacitors的意思 ferroelectric carrier的意思 ferroelectric cell的意思 ferroelectric ceramic的意思 ferroelectric ceramic capacitor的意思

Radical ring

Jacobson radical