Universal Central Extensions Of Lie-Rinehart Superalgebras

In this article, we mainly study the universal central extensions of Lie-Rinehart superalge-bras. We first give the definition and examples of Lie-Rinehart superalgebras through some pre-scribed symbols and concepts, and then we introduce the concept of action, semi-direct product,homomorphism, cross module on the definition of Lie-Rinehart superalgebras and study some properties.With these preparations, We begin to study the universal central extensions of Lie-Rinehart superalgebras. In this section, we give the definition of central extension and universal central extension, deduce their properties, obtain a characteristic description theorem(Theorem 3.1). Next, we study the functor uceA and lifting of automorphisms and derivations. Last, we in-troduce a non-abelian tensor product of Lie-Rinehart superalgebras and relate it with the universal central extension.