  We introduce the class of split Lie-Rinehart algebras as the natural
extension of the one of split Lie algebras. We show that if $L$ is a tight
split Lie-Rinehart algebra over an associative and commutative algebra $A,$
then $L$ and $A$ decompose as the orthogonal direct sums $L = \bigoplus_{i \in
I}L_i$, $A = \bigoplus_{j \in J}A_j$, where any $L_i$ is a nonzero ideal of
$L$, any $A_j$ is a nonzero ideal of $A$, and both decompositions satisfy that
for any $i \in I$ there exists a unique $\tilde{i} \in J$ such that
$A_{\tilde{i}}L_i \neq 0$. Furthermore any $L_i$ is a split Lie-Rinehart
algebra over $A_{\tilde{i}}$. Also, under mild conditions, it is shown that the
above decompositions of $L$ and $A$ are by means of the family of their,
respective, simple ideals.
