Jacobson radical

Let $𝑅$ be a ring. The Jacobson radical $J a c (𝑅)$ is defined as the intersection of the annihilators of all simple modules #m/def/ring

𝐽 (𝑅) = ⋂ 𝑀 s i m p l e 𝑅 A n n 𝑀

and is thus a two-sided ideal.

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