The product of generalized superderivations on a prime superalgebra

Abstract

In the paper, we extend the definition of generalized derivations to superalgebras and prove that a generalized superderivation g on a prime superalgebra A is represented as g(x) = ax+d(x) for all x ∈ A, where a is an element of Qmr (the maximal right ring of quotients of A) and d is a superderivation on A. Using the result we study two generalized superderivations when their product is also a generalized superderivation on a prime superalgebra A.