Abstract

This chapter presents a general approach to the structure of radicals in some ring constructions. A considerable number of results concerning radicals of various ring constructions are known in the literature. Quite a few of them have very much in common, although at first sight, they deal with fairly different constructions. It would be natural to find out the reasons of their similarity and, if possible, to obtain these results in a uniform way. In studying semigroup graded rings, it seems most interesting to know how properties of the whole ring depend on the properties of the components.

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