Abstract
In this article semisimple classes of topological algebras are characterized in a series of varieties of rings (in particular, all subvarieties of the varieties of alternative and Jordan algebras). Characterizations of semisimple classes of hereditary radicals are obtained, and the heredity of semisimple classes of radicals is demonstrated. It is proved that the construction of lower radicals stabilizes on the first infinite ordinal in the varieties of topological algebras considered.
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 14, pp. 250–261, 1989.
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Beidar, K.I., Glavatskii, S.T. & Mikhalev, A.V. Semisimple classes and lower radicals of topological nonassociative algebras. J Math Sci 51, 2487–2496 (1990). https://doi.org/10.1007/BF01097164
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DOI: https://doi.org/10.1007/BF01097164