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In this paper, a left module over an associative ring
with identity is de¯ned to be openly semiprimitive (strongly semi-
primitive, respectively) by the zero intersection of all maximal open
fully invariant submodules (all maximal open submodules which are
fully invariant, respectively) of it. For any projective module, the
openly semiprimitivity of the projective module is an equivalent
condition of the semiprimitivity of endomorphism ring of the pro-
jective module and the strongly semiprimitivity of the projective
module is an equivalent condition of the endomorphism ring of the
projective module being a subdirect product of a set of subdivisions
of division rings.
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