In this paper we propose a general setting in which to study the radical theory of group graded rings. If 31 is a radical class of associative rings we consider two associated radical classes of graded rings which are denoted by 3l G and 3l Ki . We show that if 31 is special (respectively, normal), then both 31 and 3l ni are graded special (respectively, graded normal). Also, we discuss a graded version of the ADS theorem and the termination of the Kurosh lower graded radical construction.
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