A one-sided admissible ideal radical which is almost subidempotent (Q1094511)

The author has already studied the upper radical determined by the class \(E\) of all rings without admissible ideals which are not ideals. In this interesting paper he extends his study to the upper radical determined by the class \(E_ r\) of all rings without admissible right ideals which are not right ideals. He establishes that this radical is not hereditary, is almost subidempotent, contains the upper radical determined by \(E\), is equal to the upper radical determined by the class of all division rings and of all zero rings, and is equal to the class of all idempotent \(D\)-radical rings where \(D\) is the upper radical determined by the class of all division rings. Finally, several insights are established for \(E_ r\) rings.