The product of generalized superderivations on a prime superalgebra

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 ginsert ignore into journalissuearticles values(x); = ax+dinsert ignore into journalissuearticles values(x); for all x ∈ A, where a is an element of Qmr insert ignore into journalissuearticles values(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.