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In this paper we prove that there exist paragraded rings which are not graded and we discuss prime and Jacobson radicals of paragraded rings. In particular, we prove that paragraded counterparts of prime and Jacobson radicals are the largest paragraded ideals contained in them. * This paper was presented at the International Scientific Conference Graded structures in algebra and their applications, dedicated to the memory of Prof. Marc Krasner, IUCDubrovnik, Croatia, September, 22-24, 2016.
Ilić-Georgijević et al. (Thu,) studied this question.