Quasi Z-algebraic Domain

As a common generalization of quasialgebraic posets and Z -algebraic posets, the definition of quasi Z -algebraic domain and its basic properties are investigated. One way of this paper is to generalize the basis of quasicontinuous domain theory to a general subset system Z, and its mapping characterization of quasi Z-algebraic domain is given. Furthermore, the relations between the quasi Z -continuous domain and quasi Z-algebraic domain are studied. In the last term, and we discuss the multiplication of quasi Z -continuous domain and quasi Z -algebraic domain separately..