Note on strongly Lie nilpotent rings.
Note on strongly Lie nilpotent rings.
Some results on strongly Lie nilpotent rings are given in the paper. Among them there is an analogue of P. Hall's theorem on nilpotent groups. We quote it: Let \(R\) be a ring, let \(I\) be an ideal of \(R\) such that its strong center \(F(I)\) is an ideal of \(R\) and let \(M\) be the largest ideal of \(R\) contained in the Lie square of \(I\). If \(I\) and \(R/M\) are strongly Lie nilpotent rings, then \(R\) is strongly Lie nilpotent.
- University of Salento Italy
Ring, Nil and nilpotent radicals, sets, ideals, associative rings, Central chains, strongly Lie nilpotent rings, Lie brackets, Rings with involution; Lie, Jordan and other nonassociative structures, upper central series, central chains, lower central series, Strongly Lie nilpotent ring, Ideals in associative algebras, 510
Ring, Nil and nilpotent radicals, sets, ideals, associative rings, Central chains, strongly Lie nilpotent rings, Lie brackets, Rings with involution; Lie, Jordan and other nonassociative structures, upper central series, central chains, lower central series, Strongly Lie nilpotent ring, Ideals in associative algebras, 510
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