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Radicals and Köthe’s Conjecture for Skew PBW Extensions

  • Armando ReyesEmail author
  • Héctor Suárez
Article

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.

Keywords

Armendariz rings Köthe’s conjecture Skew PBW extensions 

Mathematics Subject Classification

16S36 16S80 16N40 16U20 

Notes

Acknowledgements

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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Copyright information

© School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Nacional de ColombiaSede BogotáColombia
  2. 2.Escuela de Matemáticas y EstadísticaUniversidad Pedagógica y Tecnológica de ColombiaSede TunjaColombia

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