In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.

We introduce the class of split regular Hom-Poisson algebras formed by those Hom-Poisson algebras whose underlying Hom-Lie algebras are split and regular. This class is the natural extension of the ones of split Hom-Lie algebras and of split Poisson algebras. We show that the structure theorems for split Poisson algebras can be extended to the more general setting of split regular Hom-Poisson algebras. That is, we prove that an arbitrary split regular Hom-Poisson algebra is of the form $=U+{\sum }_j{I}_j$ with U...