ON BASE RADICAL AND SEMISIMPLE CLASSES DEFINED BY CLASS OPERATORS (vol 138, pg 307, 2013)

Regarding the article of the title, which appeared in Acta Math. Hungar., 138 (2013), 307-328, we regret to note that some of the arguments given in Section 6 are faulty. In particular, the proof of Theorem 6.3 is flawed (even if one corrects its statement to the more plausible claim that for every a is an element of A, X-b(a) is an element of S(R)). Hence also Corollaries 6.4 and 6.5 as well as Proposition 6.7 are in doubt as stated. However, the main claim of the section, that every base radical/semisimple pair arises from a Hoehnke radical is still correct, although a different proof is required. In particular the stated definition of X-b must be altered in order that the arguments work. (Perhaps the earlier definition can be made to work, but we do not see how.) We repeat the general definition of a Hoehnke radical operation on a universal class below, and follow it with the needed new arguments.