Конструкция Херстейна для почти конечномерных супералгебр

The connections between semiprime associative $Z_{2}$-graded algebras and Jordan superalgebras are studied. It is proved that if an adjoint Jordan superalgebra $B^{(+)_{s}}$ to an associative noncommutative $Z_{2}$-graded semiprime superalgebra $B$ contains an ideal, consisted of odd elements, then the center of algebra $B$ contains a nonzero ideal. Besides, this ideal annihilates every commutator of the algebra $B$. As a corollary we have that if a $Z_{2}$-graded algebra $B$ is just infinite then a Jordan superalgebra $B^{(+)_{s}}$ is just infinite.