Radicals of paragraded rings

This paper is concerned with the theory of paragraded rings, which begins with a series of Krasner and Vuković's notes in Proceedings of the Japan Academy, which first appeared in late 1980s. We present prime and Jacobson radicals, discuss the general Kurosh–Amitsur theory of radicals of paragraded rings, establish that the theorem of Anderson, Divinsky, and Suliński holds for paragraded rings, characterise paragraded normal radicals, and prove that all special paragraded radicals of paragraded rings can be described by appropriate classes of their graded modules.