Abstract
An associative ring R, not necessarily with an identity element, is called semilocal if R modulo its Jacobson radical is an artinian ring. It is proved that if the adjoint group of a semilocal ring R is locally supersoluble, then R is locally Lie-supersoluble and its Jacobson radical is contained in a locally Lie-nilpotent ideal of finite index in R.
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Catino, F., Miccoli, M.M. & Sysak, Y.P. Semilocal rings whose adjoint group is locally supersoluble. Arch. Math. 95, 213–224 (2010). https://doi.org/10.1007/s00013-010-0158-5
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DOI: https://doi.org/10.1007/s00013-010-0158-5