The Intersection of the Powers of the Topological Jacobson Radical and Topological Krull Dimension
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In this paper, it is proved that a certain power of the topological Jacobson radical for a ring annihilates a left module having topological Krull dimension over this ring. The estimation of this power depends on the topological Krull dimension and the dual topological Krull dimension. A similar estimation for discrete Jacobson radical holds true. Levitzky’s theorem is generalized for topological rings.
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- 4.N. Jacobson, “The radical and the semi-simplicity for arbitrary rings,” Am. J. Math., No. 67, 300–320 (1945).Google Scholar