Abstract
A note on sandwich Engel conditions on Lie ideals in semiprime rings
Highlights
Let R be a prime ring, Z(R) its center, U its left Utumi quotient ring, C the center of U and d a non-zero derivation of R
We examine the case R is a 2-torsion free semiprime ring and [z, t]m[d([x, y]), [x, y]]k [z, t]n = 0, for all x, y, z, t ∈ R
A well known result of Posner [14] states that if the commutator [d(x), x] ∈ Z(R), the center of R, for any x ∈ R, R is commutative. This theorem indicates how the global structure of a ring R is often tightly connected to the behaviour of additive mappings defined on R
Summary
Department of Legal, Historical, Economic and Social Sciences Magna Graecia University of Catanzaro Copyright c 2013 Francesco Rania. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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