(untitled) (Communications in Mathematical Research, 2021)
In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. According to the decomposition of n-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of n-Lie superalgebras, so we can see its application in the decomposition of n-Lie superalgebras.