Let R be a prime ring of characteristic ≠ 2 with a derivation d ≠ 0, L a non central Lie ideal of R such that [d(u), u]n is central, for all u ∈ L. We prove that R must satisfy s4 the standard identity in 4 variables. We also examine the case R is a 2-torsion free semiprime ring and [d([x, y]), [x, y]]n is central, for all x, y ∈ R.
Commutators with power central values on a Lie ideal
CARINI, Luisa;DE FILIPPIS, Vincenzo
2000-01-01
Abstract
Let R be a prime ring of characteristic ≠ 2 with a derivation d ≠ 0, L a non central Lie ideal of R such that [d(u), u]n is central, for all u ∈ L. We prove that R must satisfy s4 the standard identity in 4 variables. We also examine the case R is a 2-torsion free semiprime ring and [d([x, y]), [x, y]]n is central, for all x, y ∈ R.File in questo prodotto:
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