Algebraically generated superalgebras

A simple right-alternative superalgebra whose even part has zero multiplication is called singular. In the paper, finite-dimensional algebraically generated singular superalgebras with a non-degenerate switch are introduced and studied. A special case of such algebras, namely, linearly generated superalgebras, was previously classified by the authors. The construction of the extended double is given in the paper and it is proved that an algebraically generated singular superalgebra with a non-degenerate switch is an extended double. It is also shown that for any number $d\geq32$ there exists a $d$ -dimensional extended double.