Extending torsion radicals

Over an arbitrary ring R, a symmetric radical is shown to be strongly normalizing. For a fully semiprimary Noetherian ring R, a symmetric radical is normalizing if and only if the class of torsion factor rings of R is closed under ring isomorphisms. In case S is a strongly normalizing or normalizing extension ring of R, a symmetric radical for S is constructed as an extension of a symmetric radical for R. Applications address questions concerning the behavior of Krull dimension and linked prime ideals of S.