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 andcoprime element. Then it is shown that the concepts of the second element and coprimeelement are equivalent. Moreover, this study gives us a characterization of comultiplicationmodules. Finally, it defines pure elements and obtains the relation among pure, idempotentand multiplication elements.