Universal Central Extensions and Non-abelian tensor product of Hom-Lie-Rinehart Algebras

In this paper we study universal central extensions and non-abelian tensor product of hom-Lie-Rinehart algebras. We discuss about universal $\alpha$- central extensions, and, lifting of automorphisms and $\alpha$-derivations to central extensions for hom-Lie-Rinehart algebras. This is in turn provide such lifting of automorphisms and ${\alpha }^k$-derivations to the central extensions for hom-Lie algebras.