A generalization of semi prime indeals in γ-rings

The purpose of this paper is to generalize the concept of semi prime ideals in Γ-rings. We use a general definition of a regularity F for Γ-rings to define and F- prime ideal. Relationships between F-semi prime ideals of a Γ-ring M and F-semi prime ideals of the operator rings R and L are discussed. D-regularity, f-regularity and λ-regularity for Γ-rings are introduced and studied against the background of the concept F-semi prime ideal. Finally, D-, λ- and f-regular Γ-rings are characterized.