Abstract
The aim of this paper is to investigate different radicals (Wedderburn radical, lower nil radical, Levitzky radical, upper nil radical, the set of all nilpotent elements, the sum of all nil left ideals) of the noncommutative rings known as skew Poincaré–Birkhoff–Witt extensions. We characterize minimal prime ideals of these rings and prove that the Köthe’s conjecture holds for these extensions. Finally, we establish the transfer of several ring-theoretical properties (reduced, symmetric, reversible, 2-primal) from the coefficients ring of a skew PBW extension to the extension itself.
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The first author was supported by the research fund of Facultad de Ciencias, Code HERMES 41535, Universidad Nacional de Colombia, Bogotá, Colombia.
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Reyes, A., Suárez, H. Radicals and Köthe’s Conjecture for Skew PBW Extensions. Commun. Math. Stat. 9, 119–138 (2021). https://doi.org/10.1007/s40304-019-00189-0
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DOI: https://doi.org/10.1007/s40304-019-00189-0