  We give an interpretation of the Brauer group of a purely inseparable
extension of exponent 1, in terms of restricted Lie-Rinehart cohomology. In
particular, we define and study the category $p$-$\rm{LR}(A)$ of restricted
Lie-Rinehart algebras over a commutative algebra $A$. We define cotriple
cohomology groups $H_{p-LR}(L,M)$ for $L\in p$-$\rm{LR}(A)$ and $M$ a Beck
$L$-module. We classify restricted Lie-Rinehart extensions. Thus, we obtain a
classification theorem for regular extensions considered by Hoshschild.
