A comparison of Kurosh-Amitsur and base radical classes

In this paper we use class operators to compare and contrast Kurosh-Amitsur radical classes and base radical classes in a setting where they do not coincide to highlight some of the consequences of changing 'ideal' to 'accessible' in the construction. We show the result of Puczylowski that the largest hereditary subclass of a Kurosh-Amitsur radical class is a Kurosh-Amitsur radical class does not extend to the largest hereditary subclass of a base radical class being base radical and uncover a class of algebras which are not Kurosh-Amitsur radical-semisimple, nor base radical-semisimple, but rather Kurosh-Amitsur radical-base semisimple.