On Lattices of Radical Rings

In this dissertation we proved some of results and theorems about the lattice of radicals of rings. To answer on the questions of J.M.Rjabuhin in [13 ]: Is the lattice of special radicals S is a Boolean lattice? What is the relationship between the lattice of special radicals S and the lattice of special radical classes SC? Is the lattice of special radicals which is Generated by *-ring is an atomic lattice? For that we showed that the lattice of all radicals L is not a modular lattice, so it is not a Boolean one. And we gived examples show that all of the lattices of hereditary , overnilpotent and special radicals are not complemented lattices , so also they are not Boolean ones; so we answered the first question. And we proved that all the atoms in the lattice of hereditary radicals are as l_Q where Q is a simple ring.