Abstract
Let R be a commutative associative ring with 1 and let Der ( R ) be the Lie ring of all derivations of R. Suppose that D is a Lie subring and an R-submodule of Der ( R ) . When R is D-prime, we give necessary and sufficient conditions for D to be Lie prime. Since results of this nature are already known for rings R of characteristic different from 2, what is really new here is the characteristic 2 case.
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