ON REVERSIBILITY OF RINGS WITH INVOLUTION

Abstract

Let R be a ring with involution *. We give the notion of central *-reversible *-rings which generalizes weakly *-reversible *-rings. Moreover, we introduce the class of weakly *-rings which is a generalization of central *-reversible *-rings and investigate their properties. Further, a generalization of the class of quasi-*-IFP *-rings is given; namely weakly quasi-*-IFP *-rings. Since every *-reversible *-ring is central *-reversible, we give sufficient conditions for central *-reversible, weakly *-reversible and weakly quasi-*-IFP *-rings to be *-reversible and some examples are given to illustrate these situations. Finally, we show that the properties of *-reversible, central *-reversible, weakly *-reversible and weakly quasi-*-IFP can be transfer to some extensions of the *-ring.