On a Class of -Modules

In [Int. Electron. J. Algebra, 15, 173 (2014)], Smith introduced maps between the lattice of ideals of a commutative ring and the lattice of submodules of an R-module M, i.e., μ and 𝜆 mappings. The definitions of the maps were motivated by the definition of multiplication modules. Moreover, some sufficient conditions for the maps to be lattice homomorphisms were studied. We define a class of 𝜆-modules and indicate the properties of this class. We also present sufficient conditions for the module and the ring under which the class 𝜆 is a hereditary pretorsion class.