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High Quality Content by WIKIPEDIA articles 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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