Sergey Pchelintsev
Finance University under the Government of the Russian Federation
Prime degenerate algebras.
Abstract: The structure of prime nondegenerate algebras in the principal varieties of nearly associative algebras is described by the classical theorems by M.Slater (alternative algebras), I.Hentzel ((-1,1)-algebras) and E.Zelmanov (Jordan algebras). The problem of the existence of prime degenerate algebras in these varieties was positively resolved by the speaker who constructed examples of such algebras. K.McCrimmon called these examples monsters . Later Yu.Medvedev, E.Zelmanov, and I.Shestakov gave another constructions of monsters. Now we proved that, over a field of characteristic 0, the different monster constructions in varieties of (-1,1)-algebras and Jordan algebras in fact produced isomorphic algebras. In the case of alternative algebras, there are infinitely many non-isomorphic prime commutative algebras, and there are infinite series of identities that separate prime non-commutative algebras.