# Ideal categories of rings and ring of cones

## TL;DR

This paper explores the structure of the ideal category of a ring R, showing it forms a preadditive proper category, and demonstrates that cones within this category constitute a ring with suitable operations.

## Contribution

It introduces a novel perspective by characterizing the ideal category as a preadditive proper category and establishing the ring structure of cones within it.

## Key findings

- The ideal category of a ring R can be described as a preadditive proper category.
- Cones in this category form a ring with defined addition and multiplication.
- Provides a new categorical framework for understanding ring structures.

## Abstract

In this paper we describe the ideal category of a ring R as preadditive proper category. Further it is also shown that the cones in this category is a ring with appropriate addition and multiplication.