ON REVERSIBILITY OF RINGS WITHINVOLUTION

Abstract

Let
R
be a ring with involution *. We give the notion of central
*-reversible *-rings which generalizes weakly *-reversible *-rings. More-
over, 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 proper-
ties of *-reversible, central *-reversible, weakly *-reversible and weakly
quasi-*-IFP can be transfer to some extensions of the *-ring.