# Quasi-Primary Spectrum of a Commutative Ring and a Sheaf of Rings

## TL;DR

This paper introduces the quasi-primary spectrum of a commutative ring, explores its topological properties, and constructs a sheaf of rings on it, linking it to the prime spectrum.

## Contribution

It defines the quasi-primary spectrum, studies its topology, and constructs a sheaf of rings that relates to the prime spectrum, extending the algebraic geometric framework.

## Key findings

- Quasi-primary spectrum has interesting topological properties.
- A sheaf of rings on the quasi-primary spectrum is constructed.
- The sheaf is shown to be the direct image sheaf from the prime spectrum.

## Abstract

In this work, the set of quasi-primary ideals of a commutative ring with identity is equipped with a topology and is called quasi-primary spectrum. Some topological properties of this space are examined. Further, a sheaf of rings on the quasi-primary spectrum is constructed and it is shown that this sheaf is the direct image sheaf with respect to the inclusion map from the prime spectrum of a ring to the quasi-primary spectrum of the same ring.