On Weakly Fπ-Regular and Weakly wFπ-Regular Rings

A. The purpose of this paper is to study a new class of regular rings, namely weakly F-regular and weakly wF-regular rings.Their key properties and features, as well as the relationship between these rings and other rings, such as CS-rings, F GP -rings, and GM P -rings are investigated.Moreover, a new class of sets is introduced, namely weakly motivating and weakly w-motivating sets, after which their connections with the weakly F-regular and the weakly wF-regular rings are also studied.Weakly F*-regular and weakly wF*-regular rings are discussed, alongside their relationships with weakly F-regular and weakly wF-regular rings.2-primal rings are classified, and the conditions required to render the 2-primal weakly F-regular and weakly wF-regular rings are also examined.2020 Mathematics