Equations Related to Superderivations on Prime Superalgebras - Fošner, Ajda; Fošner, Maja (MATHEMATICA SCANDINAVICA, 2014)
In this paper we investigate equations related to superderivations on prime superalgebras. We prove the following result. Let D=D_0+D_1 be a nonzero superderivation on a prime associative superalgebra A satisfying the relations D_i(x)[D_i(x),x]_s=0, [D_i(x),x]_sD_i(x)=0 for all xA, i=0,1. Then one of the following is true: (a) A_1=0 and D(A_0) Z(A) or (b) D(A_0)=0 and A is commutative or (c) D^2=0. The research is a generalization of the results in [10] and [4] by using the theory of superalgebras.