  A classical theorem of Veldkamp describes the center of an enveloping algebra
of a Lie algebra of a semi-simple algebraic group in characteristic $p.$ We
generalize this result to a class of Lie algebras with a property that they
arise as the reduction modulo $p\gg 0$ from an algebraic Lie algebra
$\mathfrak{g},$ such that $\mathfrak{g}$ has no nontrivial semi-invariants in
$Sym(\mathfrak{g})$ and $Sym(\mathfrak{g})^{\mathfrak{g}}$ is a polynomial
algebra.
  As an application, we solve the derived isomorphism problem of enveloping
algebras for the above class of Lie algebras.
