ON STRONGLY RIGHT π-DUO RINGS

This article continues the study of right π-duo rings, concentrating on the situation of nonzero powers. For this purpose we introduce the concept of strongly right π-duo and examine the structure of strongly right π-duo in relation to various ring properties that play important roles in ring theory. It is proved for a strongly right π-duo ring R that if the upper (lower) nilradical of R is zero then R is reduced. Various kinds of examples are examined in relation to the questions raised in the procedure.