Journal of the
Korean Mathematical Society JKMS

A ring is a DICC ring if every chain of right ideals indexed by the integers stabilizes to the left or to the right or to both sides. A counterexample is given to an assertion of Karamzadeh and Motamedi that a transfinite power of the Jacobson radical of a right DICC ring is zero. We determine the behavior of the trans-finite powers of the Jacobson radical relative to a torsion theory and consequently can obtain their correct behavior in the classical setting.

Keywords: Jacobson radical, torsion theory, DICC module