ON SYMMETRIC RADICALS OVER FULLY SEMIPRIMARY NOETHERIAN RINGS

Symmetric radicals over a fully semiprimary Noetherian ring R are characterized in terms of stability on bimodules and link closure of special classes of prime ideals. The notion of subdirect irreduciblity with respect to a torsion radical is introduced and is shown to be invariant under internal bonds between prime ideals. An analog of the Jacobson radical is produced which is properly larger than the Jacobson radical, yet satisfies the conclusion of Jacobson's conjecture for right fully semiprimary Noetherian rings.