ON A CLASS OF RADICALS OF RINGS

Let lambda be a property that a lattice of submodules of a module may possess and which is preserved under taking sublattices and isomorphic images of such lattices and is satisfied by the lattice of subgroups of the group of integer numbers. For a ring R the lower radical Lambda generated by the class lambda(R) of R-modules whose lattice of submod ules possesses the property lambda is considered. This radical determi nes the unique ideal Lambda(R) of R, called the lambda-radical of R. W e show that Lambda is a Hoehnke radical of rings. Although generally L ambda is not a Kurosh-Amitsur radical, it has the ADS-property and the class of Lambda-radical rings is closed under extensions. We prove th at Lambda(M(n)(R))subset of or equal to M(n)(Lambda(R)) and give some illustrative examples.