Second and Secondary Lattice Modules

Abstract

Let M be a lattice module over the multiplicative lattice L . A nonzero L -lattice module M is called second if for each a ∈ L , a 1 M = 1 M or a 1 M = 0 M . A nonzero L- lattice module M is called secondary if for each a ∈ L , a 1 M = 1 M or a n 1 M = 0 M for some n > 0 . Our objective is to investigative properties of second and secondary lattice modules.