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

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.