Main Index
Algebraic structures
Ring theory
Basic notions
Subject Index
comment on the page
The Jacobson radical of a ring
with identity is defined by one of the following equivalent ways:
The Jacobson radical is named for Nathan Jacobson , who first defined and studied the Jacobson radical.
If ring does not have identity, then the definition of the Jacobson ideal is more involved. First define the binary operation on
by
for all
. Then
is a semigroup with an identity element. Then the Jacobson radical is defined to be the largest ideal
of
such that
is a subgroup of
.
Cite this web-page as:
Štefan Porubský: The Jacobson radical.