We show that the radical and nilradical bundles are characteristic ideal bundles of a Lie algebra bundle. Further a Lie algebra bundle is semisimple if and only if its derivation algebra bundle is semisimple.
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B. Sa Kiranagi, Prema, Gb, and Ranjitha, Ka, “On the radical bundle of a Lie algebra bundle”, Proceedings of the Jangjeon Mathematical Society, vol. 15, pp. 447-453, 2012.