A Zariski-like topology on the 2-prime spectrum of commutative rings

Document Type : Research Paper

Authors

1 arak university of technology

2 Arak university of technology

Abstract

A proper ideal P of a ring R is called \emph{2-prime} if for all x,yR such that xyP, then either x2P or y2P. In this paper, we introduce a Zariski topology on the set of all 2-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.

Keywords