Abelian dqt-groups and rings on them

The absolute radical of an Abelian group $G$ is the intersection of radicals of all associative rings with additive group $G$. The problem of describing absolute radicals was formulated by L. Fuchs. He described the absolute Jacobson radical of a torsion Abelian group. In this work, the absolute Jacobson radical and the absolute nil-radical are investigated in some mixed Abelian group classes.