A Certain Expansion of Positive Cone of Partially ordered Linear Spaces

Let E be a parｔially ordered ｌinear space in a most general sense. We define the set P in E such that P＝{x: x＜y implies y≧0}. In section 1, we shall consider about some necessary conditions which yield to that P＝E^+. In section 2, we shall investigate about some properties of P. And assuming that P satisfies conditions of positive cone of partially ordered linear space, we shall make properties of ordering which is introduced by P clear. Finally we shall get necessary and suffcient condition of that P=E^+.