Abstract.
The set of all elements of an associative ring R, not necessarily with a unit element, forms a monoid under the circle operation a ° b = a + b + ab. The group of all invertible elements of this monoid is called the adjoint group of R and is denoted by R °. It is proved that an artinian ring R with supersolvable adjoint group R ° must be Lie supersolvable. An example of a Lie supersolvable ring with non-supersolvable adjoint group is also constructed.
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Received: 7 December 2007
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Ievstafiev, R.I. Artinian rings with supersolvable adjoint group. Arch. Math. 91, 12–19 (2008). https://doi.org/10.1007/s00013-008-2679-8
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DOI: https://doi.org/10.1007/s00013-008-2679-8