Pure Elements and Dual Notions of Prime Elements in Lattice Modules

Abstract

This paper deals with the pure elements and the dual notions of prime elements (that is, second elements). For this, it introduces the definitions of second element and coprime element. Then it is shown that the concepts of the second element and coprime element are equivalent. Moreover, this study gives us a characterization of comultiplication modules. Finally, it defines pure elements and obtains the relation among pure, idempotent and multiplication elements.