On semi-NI rings

چکیده مقاله

In this Paper, we first introduce the concept of semi-NI rings which is a generalization of NI rings, and then we examine the characteristics of this class of rings. We investigate relationships between semi-NI rings and some other known classes of rings. We show that the class of semi-NI rings lies strictly between the class of NI rings and the class of directly finite rings. Also, we prove that this class of rings lies strictly between the class of NI rings and the class of NCI rings. In the following, we show that semi-NI rings are characterized by many equivalent conditions.