Some External Characterizations of SV-Rings and Hereditary Rings

In ring theory, the notion of annihilator is an important tool for studying the structures. Many characterizations and structure theorems can be derived by using this notion. On the other hand, certain classes of rings (e.g., Baer rings and Rickart rings) are defined by considering annihilators ideals. In the present work, we introduce a class of rings which is close to the class of Rickart rings. We then investigate endomorphism rings having this property. This will enable us to obtain characterizations of certain classes of rings, namely the SV-rings and the hereditary rings. We have divided this work into three sections. In the first we give some preliminary results and examples. In the second, we characterize SV-rings. The third section is devoted to hereditary rings.