Minimal prime ideals in enveloping algebras of Lie superalgebras

Let g be a finite dimensional Lie superalgebra over a field of characteristic zero. Let U(g) be the enveloping algebra of g. We show that when g = b(n), then U(g) is not semiprime, but it has a unique minimal prime ideal; it follows then that when g is classically simple, U(g) has a unique minimal prime ideal. We further show that when g is a finite dimensional nilpotent Lie superalgebra, then U(g) has a unique minimal prime ideal.