ابوالفضل تاری زاده

In this paper, we de ne the new notion of quasi-prime ideal which generalizesat once both prime ideal and primary ideal notions. Then a natural topology on the set ofquasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspacetopology. The basic properties of the quasi-prime spectrum are studied and several interestingresults are obtained. Specially, it is proved that if the Grothendieck t-functor is applied onthe quasi-prime spectrum then the prime spectrum is deduced. It is also shown that thereare the cases that the prime spectrum and quasi-prime spectrum do not behave similarly. Inparticular, natural topological spaces without closed points are obtained.