The Wedderburn decomposition in finite-dimensional alternative superalgebras of characteristic 3

The Wedderburn decomposition in finite dimensional alternative superalgebras of characteristic 3 is studied. It is proved that the decomposition exists provided the semisimple quotient superalgebra does not contain certain simple superalgebras. Counterexamples are given which show that the restrictions cannot be omitted. Together with the similar results by N.A.Pisarenko for the characteristic not equal 2,3 case, the results of the paper give a description of Wedderburn decomposition for alternative superalgebras of characteristic not equal 2.