An identity in prime superalgebras
In this paper we investigate the functional identity in a prime associative superalgebras. We prove the following result. Suppose that there exists a nonzero additive mapping f = f0+f1, on a prime associative superalgebra A with char(R)≠2, satisfying the relation [f(x); y2] = 0 for all x, y ∈ H(A). If
- A is prime algebra then [f(A);A] = 0 or [A;A] = 0.
- A0 is prime algebra then [f(A);A] = 0 and [A;A0] = 0 or A is trivial. More-over, if C1 = 0 then f0(A1) = 0 and f1(A0) = 0.
Mathematics Subject Classification (2010): 17A70, 17B01, 17B40.
Keywords: Superalgebra, prime superalgebra, semiprime superalgebra, superderivation, supercommutator, extended centroid