Jordan superderivations. II.
In a recent paper the author proved that a Jordan superderivation \(D\) on a prime associative superalgebra \(A=A_0\oplus A_1\) is a superderivation, unless the even part \(A_0\) is commutative [part I, Commun. Algebra 31, No. 9, 4533-4545 (2003; Zbl 1048.16016)]. In the paper under review this result is extended to the semiprime case. The main result in particular shows that there exist two graded ideals \(U\) and \(V\) such that their direct sum is an essential ideal of \(A\), the restriction of \(D\) to \(U\) is a superderivation, and \(V\) has a commutative even part. By an example the author also justifies the restriction to an essential ideal.
scientific article; zbMATH DE number 2171597