On seminoetherian noncommutative rings and modules

The purpose of this article is to present the results of the study conducted by [1] within a noncommutative context. That is, we study left seminoetherian rings and left sufficiently noetherian rings. We give examples of these two types of rings that no satisfy the respective condition on the other side. We also show that the class of left sufficiently noetherian modules is the natural class generated by noetherian modules.