On a class of -modules

UDC 512.5 Smith in paper [{\it Mapping between module lattices}, Int. Electron. J. Algebra, {\bf 15}, 173–195 (2014)] introduced maps between the lattice of ideals of a commutative ring and the lattice of submodules of an $R$-module $M,$ i.e., $\mu$ and $\lambda$ mappings. The definitions of the maps were motivated by the definition of multiplication modules. Moreover, some sufficient conditions for the maps to be a lattice homomorphisms are studied. In this work we define a class of $\lambda$-modules and observe the properties of the class. We give a sufficient conditions for the module and the ring such that the class $\lambda$ is a hereditary pretorsion class.