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 Jacobson 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 .