The theory of radicals of topological rings began to develop by an analogy to the theory of radicals of discrete rings i.e. rings without topology. The majority of results of the theory of radicals of topological rings had the analogues in the discrete case. However presence of topology and the requirement of the closedness of some ideals have Given the specificity of the theory of radicals of topological rings. So some results of the Theory of radicals of topological rings are trivial in a discrete case (see, for example, results Stated in I. 4 and II. 8). One of the specific questions of the theory of radicals of topological Rings is the fact that the theory of radicals can be applied to the description of the topology Of the ring.
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