algebraic and topological aspects of quasi-prime ideals

In this paper, we define the new notion of quasiprime ideal which generalizes at once both prime ideal and primary ideal notions. then a natural topology on the set of quasiprime ideals of a ring is introduced which admits the zariski topology as a subspace topology. the basic properties of the quasiprime spectrum are studied and several interesting results are obtained. specially, it is proved that if the grothendieck tfunctor is applied on the quasiprime spectrum then the prime spectrum is deduced. it is also shown that there are the cases that the prime spectrum and quasiprime spectrum do not behave similarly. in particular, natural topological spaces without closed points are obtained.