Semi-Hereditary Ring Related Other Rings Have Ideals is Principles and Projective

Abstract

In this article, we study many relationships between semi-hereditary ring (shortly S-H-ring) and other rings which have some properties of an ideal of the ring R. We prove that if R is semi-simple with Ore property, this leads the ring R is S-H-ring. On the other hand, Q-ring with some properties of L-F-group imply to S-H-ring property. Finally, some new results and more definitions with important examples have been presented.