Ascendant subalgebras of hyperfinite Lie algebras (Q1191886)

If \(H\) is a subalgebra of a hyperfinite Lie algebra \(L\) the author proves that \(H\) is ascendant (weakly ascendant) if and only if it is serial (weakly serial) and that the intersection of any family of ascendant (weakly ascendant) subalgebras of \(L\) is ascendant (weakly ascendant). It is also shown that in a hyperfinite-by-abelian Lie algebra over a field of characteristic zero, the join and the intersection of any family of ascendant subalgebras is always ascendant.