Studies in Rings generalised Unique Factorisation Rings

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Definition 1 029.
An ideal P in a ring R is said to be
right (left)
Qximitive pr0vided P = ann RA for some simple right
(left) R-module A.
A right (left) primitive ring is
any ring in which 0 is a primitive ideal, ie. any ring
with a
faithful, simple right (left) R-module.
Proposition 1 030.
In any ring R,
the following sets coincide:
(a)
(b)
The intersection of all maximal right ideals.
The intersection of all ma x ima 1 left ideals.
( c) The intersection of all right primitive ideals.
(d) The intersection of all left primitive ideals.
Definition 1 0:31.
A ring R is semiprimitive (Jacobson Se~i5imple) if
and only if the Jacobson radical J(R) of R is equal to
zero where J(R) is the intersection defined in proposition 1.30.
SEMISIMPLE RINGS
Vector spaces, when viewed module theoretically,