Anchor Radicals and Metric Rigidity in $n$-Lie--Rinehart Algebras

For an $n$-Lie--Rinehart algebra, $n>2$, the anchor is defined on $\Aext{n-1}L$, so its kernel does not determine a distinguished submodule of $L$. We introduce the anchor radical $\Rad(ρ)\subset L$ and prove that it is an adjoint-stable ideal on which the bracket is $A$-multilinear. We then derive