On Spectral Torsion Theories

The purpose of this thesis was to investigate how “spectralness” properties of a torsion theory on R-Mod are reflected by properties of the ring R and its ring of quotients. The study draws much more on the work of Zelmanowitz and Gomez-Pardo. Gomez-Pardo proved that there exists a bijective correspondence between the set of spectral torsion theories on R -Mod and rings of quotients of R that are Von Neumann regular and left self-injective. Within this study, we showed that an investigation on an arbitrary spectral torsion theory on R-Mod reduces to the study of the Goldie torsion theory on the category of modules over a suitable factor ring.This book is most useful for those who are interested in Mathematics, especially in rings and modules theory.