  In this paper, the new concept of quasi-prime ideal is introduced which at
the same time generalizes the `prime ideal' and `primary ideal' notions. Then a
natural topology on the set of quasi-prime ideals of a ring is introduced which
generalizes the Zariski topology. The basic properties of the quasi-prime
spectrum are studied and several interesting results are obtained. Specially,
it is proved that if the Grothendieck t-functor is applied on the quasi-prime
spectrum then the prime spectrum is deduced. It is also shown that there are
the cases that the prime spectrum and quasi-prime spectrum do not behave
similarly.
