Abstract
In this paper we use class operators to compare and contrast Kurosh-Amitsur radical classes and base radical classes in a setting where they do not coincide to highlight some of the consequences of changing ‘ideal’ to ‘accessible’ in the construction. We show the result of Puczyłowski that the largest hereditary subclass of a Kurosh–Amitsur radical class is a Kurosh–Amitsur radical class does not extend to the largest hereditary subclass of a base radical class being base radical and uncover a class of algebras which are not Kurosh–Amitsur radical-semisimple, nor base radical-semisimple, but rather Kurosh–Amitsur radical-base semisimple.
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The authors would like to thank the Reviewer for the comments and suggestions which greatly improved the accessibility of the new material.
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McDougall, R.G., Thornton, L.K. A comparison of Kurosh–Amitsur and base radical classes. Beitr Algebra Geom 62, 871–882 (2021). https://doi.org/10.1007/s13366-020-00538-z
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DOI: https://doi.org/10.1007/s13366-020-00538-z