A Zariski-like topology on the ۲-prime spectrum of commutative rings

A proper ideal P of a ring R is called \emph{۲-prime} if for all x, y \in R such that xy\in P, then either x^۲ \in P or y^۲ \in P. In this paper, we introduce a Zariski topology on the set of all ۲-prime ideals of commutative rings. We investigate this topology and clarify the interplay between the properties of this topological space and the algebraic properties of the ring under consideration.

کلیدواژه ها:

۲-prime ideal ، ۲-Zariski topology ، radical