On the simplicity of Lie algebras of derivations of commutative algebras (Q1570363)

The author previously proved [J. Lond. Math. Soc. 33, 33-39 (1986; Zbl 0591.17007)] that for \(k\) a field and \(R\) a commutative, associative \(k\)-algebra with identity and \(D\) both a Lie subalgebra and an \(R\)-submodule of \(\text{Der}_k R\), if \(R\) is \(D\)-simple (i.e. has no nontrivial proper ideals invariant under the action of \(D\)) and \(\operatorname {char} k \not= 2\), then \(D\) is a simple Lie algebra. Observing that a related result of \textit{D. S. Passman} [J. Algebra 34, 682-692 (1998; Zbl 0907.17006)] is also valid in characteristic 2, the author is able to extend his previous result to characteristic 2 and to generalize a weaker form of Passman's Theorem.