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

Document Type : Research Paper

Authors

Department of Basic Sciences, Arak University of Technology, Arak, Iran

Abstract

A proper ideal $P$ of a ring $R$ is called \emph{2-prime} if for all $x, y \in R$ such that $xy\in P$, then either $x^2 \in P$ or $y^2 \in P$. 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


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