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, a1M=1M or a1M=0M. A nonzero L-lattice module M is called secondary if for each a∈L, a1M=1M or an1M=0M for some n>0. Our objective is to investigative properties of second and secondary lattice modules.