In this paper, we introduce and study a new class of submodules which unify the concepts of prime and primary
submodules. Let M be a unital module over a commutative ring R; / : LðMÞ ! LðMÞ[ ;f g be a reduction function and
d : LðRÞ ! LðRÞ be an expansion function, where LðMÞ is the lattice of all submodules of M and LðRÞ is the lattice of all
ideals of R: A proper submodule N of M is said to be a /-d-primary submodule of M if whenever am 2 N /ðNÞ for some
a 2 R and m 2 M; then either a 2 dððN : MÞÞ or m 2 N: Many properties, characterizations and examples of /-d-primary
submodules are given.