In this paper, we study relationships between generalized derivations, quasiderivations and centroids of ternary Jordan superalgebra. We prove that the generalized derivation algebras of a ternary Jordan superalgebra are the sum of quasiderivation algebras and centroids where centroids are ideals of generalized derivation algebras. We also show that quasiderivations can be embedded into larger ternary Jordan superalgebras as derivations. At the same time, some properties about centroids of ternary Jordan superalgebras are also displayed.

中文翻译：

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三元Jordan超代数的广义导数和质心

在本文中，我们研究了三元 Jordan 超代数的广义推导、拟推导和质心之间的关系。我们证明了三元 Jordan 超代数的广义推导代数是拟推导代数和质心之和，其中质心是广义推导代数的理想。我们还表明，准推导可以作为推导嵌入到更大的三元 Jordan 超代数中。同时，还展示了三元Jordan超代数质心的一些性质。