Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, more specifically ring theory, a branch of abstract algebra, the Jacobson radical of a ring, R, consists of those elements in R which annihilate all simple right R-modules. Alternatively, one could define the Jacobson radical of a ring with "left" in place of "right" in the previous sentence. Since the annihilator of a (right/left) module over a ring is necessarily a (double-sided) ideal in the ring, the Jacobson radical is necessarily a (double-sided) ideal from the previous two remarks.[3] The Jacobson radical of a ring is frequently denoted by J(R).

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