Boyle's conjecture and perfect localizations

摘要

In this article we study the behavior of left QI-rings under perfect localizations. We show that a perfect localization of a left QI-ring is a left QI-ring. We prove that Boyle's conjecture is true for left QI-rings with finite Gabriel dimension such that every hereditary torsion theory in the Gabriel filtration is perfect. As corollary, we get that Boyle's conjecture is true for left QI-rings which satisfy the restricted left socle condition, a result proved by Faith in 6.