Abstract
LetK be a class of associative topological algebras that is closed under subalgebras with the induced topology, direct products, quotients, and semidirect topological products with respect to continuous homomorphisms. If α is a radical of classK, then the following conditions are equivalent: 1) α is a topological special radical; 2) the α-semisimple algebras are topological subdirect products of prime α-semisimple algebras ofK;
This result is a corollary of a general result that establishes necessary and sufficient conditions for the radical α to have the intersection property with respect to a class of prime algebras. Bibliography: 17 titles.
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Translated fromTrudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 178–188.
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Arnautov, V.I., Beidar, K.I., Glavatskii, S.T. et al. The intersection property in the theory of radicals of topological algebras. J Math Sci 60, 1782–1789 (1992). https://doi.org/10.1007/BF01102589
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DOI: https://doi.org/10.1007/BF01102589