A radical P is called strongly
right hereditary (srh) if P(I) = I ∩ P(R) for every right ideal I of each
(not necessarily associative) ring R in a suitable universal class W. This
is a one-sided version of the concept of a strongly hereditary radical class
investigated by W.G. Leavitt and R.L. Tangeman. A discussion parallel to theirs is
obtained including a construction of the minimal srh radical class in W
containing a given class. Srh radicals are related to a new radical construction
obtained by modifying the lower radical construction of Tangeman and D.
Kreiling.
