Abstract :
In this paper we extend the concepts of two sided ideal and
right quasi-duo ring. These ideals and rings are called totally fully in-
variant and right strongly quasi-duo, respectively. Right strongly quasi-
duo rings are always right quasi-duo. We investigate the properties of
these rings and ideals and show among other things that right strongly
quasi-duo rings are classical, directly finite and co-hopfian while right
quasi duo, right duo or commutative rings do not have necessarily these
properties.
