W-algebraic poset and its properties

The concepts of W-algebraic poset and strong W-algebraic poset are introduced.The relationship among W-algebraic poset,Exact poset and algebraic poset is investigated.The image of aW-algebraic poset under an injective kernel operator preserving sups of directed sets is W-algebraic poset.It is shown that it is a strong W-algebraic domain if every point of a weak domain has a minimum local basis.It is also shown that a Scott continuous mapping of a weak domain preserves local basis if and only if it preserves Weakly way below relation.