In this paper we study the relationship between the maximal (prime)
elements of M and the maximal (prime) elements of L. We show that, if L is a
local lattice and the greatest element of M is weak principal, then M is local .
Then we define the Ja
cobson radical of M and denote it by J(M) and
we study its relationship with the Jacobson radical of L (J(L)) .
Afterwards, we define the semiprime element in a lattice module M, and we
show that the definitions of prime element and semiprime element are
equivalent when the greatest element of M is multiplication and we study the
properties equivalent to the properties of prime element in lattice module .
