  After endowing with a 3-Lie-Rinehart structure on Hom 3-Lie algebras, we
obtain a class of special
  Hom 3-Lie algebras, which have close relationships with representations of
commutative associative algebras. We provide a special class of Hom
3-Lie-Rinehart algebras, called split regular Hom 3-Lie-Rinehart algebras, and
we then characterize their structures by means of root systems and weight
systems associated to a splitting Cartan subalgebra.
