Extensions of strict partial orders in N-Groups

Abstract

AbstractAn attempt is made to extend the theory of extensions of partial orders in groups to strict partially ordered N-groups. Necessary and sufficient conditions, for a strict partial order of an N-group to have a strict full extension, and for a strict partial order of an N-group to be an intersection of strict full orders, are obtained when the partially ordered near-ring N and the N-group G satisfy the condition (− x) n = − xn for all elements x in G and positive elements n in N.