REVERSIBLE AND REFLEXIVE PROPERTIES FOR RINGS WITH INVOLUTION

摘要

In this note, we give a generalization for the class of *-IFP rings. Moreover, we introduce *-reversible and *-reflexive *-rings, which represent the involutive versions of reversible and reflexive rings and expose their properties. Nevertheless, the relation between these rings and those without involution are indicated. Moreover, a nontrivial generalization for *-reflexive *-rings is given. Finally, in *-reversible *-rings it is shown that each nilpotent element is *-nilpotent and Kothe's conjecture has a strong affirmative solution.