# On Fusible Rings

## TL;DR

This paper provides new characterizations of semiprime left Goldie rings, showing they are equivalent to being regular left fusible with finite Goldie dimension, and addresses previously posed questions in ring theory.

## Contribution

It introduces a novel characterization of semiprime left Goldie rings using the concept of regular left fusibility and Goldie dimension, answering open questions.

## Key findings

- Semiprime left Goldie rings are characterized by regular left fusibility and finite Goldie dimension.
- Two previously posed questions in the literature are answered negatively.
- The paper establishes a new equivalence involving fusible rings and Goldie rings.

## Abstract

We answer in negative two of questions posed in [4]. We also establish a new characterization of semiprime left Goldie rings by showing that a semiprime ring R is left Goldie iff it is regular left fusible and has finite left Goldie dimension.