Supercentralizing Superderivations on Prime Superalgebras

ABSTRACT

Let A = A ₀ ⊕ A ₁ be an associative superalgebra over a commutative associative ring F, and let Z _s (A) be its supercenter. An F-mapping f of A into itself is called supercentralizing on a subset S of A if x, f(x)] _s  ∈ Z _s (A) for all x ∈ S. In this article, we prove a version of Posner's theorem for supercentralizing superderivations on prime superalgebras.