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Rings having solvable adjoint groups

1970
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Proceedings of the American Mathematical Society
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Let °R denote the group of quasi-regular elements of a ring R with respect to circle operation. The following results have been proved: (1) If R is a perfect ring and °R is finitely generated solvable group then R is finite and hence °R =P\ o?io • • • oPm where Pi are pairwise commuting ^-groups. (2) Let R be a locally matrix ring or a prime ring with nonzero socle. Then °R is solvable iff R is either a field or a 2X2 matrix ring over a field having at most 3 elements. For a ring R let JiR)

doi:10.1090/s0002-9939-1970-0271154-6
fatcat:ftwwfspgmrflpayllaowamxzwy