  Let $\ggg=\ggg_\bz+\ggg_\bo$ be a basic classical Lie superalgebra over an
algebraically closed field $k$ of characteristic $p>2$, and $G$ be an algebraic
supergroup satisfying $\Lie(G)=\ggg$, with the purely even subgroup $G_\ev$
which is a reductive group. The center $\cz:=\cz(\ggg)$ of the universal
enveloping algebra of $\ggg$ easily turns out to be a domain. In this paper, we
prove that the quotient field of $\cz$ coincides with that of the subalgebra
generated by the $G_{\ev}$-invariant ring $\cz^{G_\ev}$ of $\cz$ and the
$p$-center $\cz_0$ of $U(\ggg_\bz)$.
