Mutations of ordinary torsion theories and generalized torsion theories connected by a Serre subcategory

TL;DR

This paper explores the relationship between ordinary and generalized torsion theories, focusing on mutations via Serre subcategories, and identifies conditions under which they coincide or transform into each other.

Contribution

It provides new insights into when generalized torsion theories derived from mutations are actually ordinary torsion theories, and vice versa.

Findings

Conditions identified for generalized torsion theories to be ordinary

Criteria for mutual transformation of torsion theories

Extension of mutation techniques to broader torsion theory classes

Abstract

Understanding how torsion theories are described and constructed is crucial to the study of torsion theory. Mutations of torsion theories have been studied as a method of constructing another torsion theory from a given one. We have already obtained how to mutate ordinary torsion theories into generalized torsion theories associated with a Serre subcategory. The paper investigates when the generalized torsion theories give ordinary torsion theories and when ordinary torsion theories provide each other.