2018/12/06 by Tarizadeh, Abolfazl, Aghajani, Mohsen
#13A99 #14A05 #18A99 #54A05 #54A10 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1812.02456
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.