A Note on Primary Spectrum Over Commutative Rings

TL;DR

This paper introduces a primary spectrum for commutative rings, explores its topological properties, and compares it with the prime spectrum to deepen understanding of ring structures.

Contribution

It defines a primary spectrum with Zariski topology and analyzes its properties, providing new insights into the structure of commutative rings.

Findings

Primary spectrum defined with Zariski topology

Differences identified between prime and primary spectra

Topological properties of the primary spectrum examined

Abstract

In this work we define a primary spectrum of a commutative ring R with its Zariski topology $\mathfrak{T}$. We introduce several properties and examine some topological features of this concept. We also investigate differences between the prime spectrum and our primary spectrum.