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On the semigroup nilpotency and the Lie nilpotency of associative algebras
Mathematical Notes, 1997This paper studies the relation between Lie nilpotence and semigroup nilpotence of associative rings. An associative ring \(R\) can be viewed as a Lie ring \(R^{(-)}\) using the multiplication \([a,b]=ab-ba\), and so the notion of the Lie nilpotence of \(R^{(-)}\) makes sense.
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1958
Bruck [70] contains a theory of nilpotency of loops which embodies some of the basic features of nilpotency for groups. We shall sketch a less general approach which seems conceptually simpler. Let 𝕷 be any class of loops such that: (a) Every subloop of a member of 𝕷 is in 𝕷.
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Bruck [70] contains a theory of nilpotency of loops which embodies some of the basic features of nilpotency for groups. We shall sketch a less general approach which seems conceptually simpler. Let 𝕷 be any class of loops such that: (a) Every subloop of a member of 𝕷 is in 𝕷.
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Nilpotent actions on nilpotent groups [PDF]
, 1975 Peter Hilton, Peter Hilton, Peter Hilton
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