Pure and Weakly Pure Elements in Lattice Modules

Abstract

This study concerns with investigation of Pure and Weakly pure elements of  lattice modules. An element N of M is called pure, if aN = N ∧ a1_M , for each a of L. An element K of M is called weakly pure, if aN = N ∧ a1_M , for each idempotent element a of L. Also, this study obtains the relation between pure, idempotent and multiplication elements of lattice modules.