Central orders in simple finite dimensional superalgebras

Abstract

The well-known Formanek's module finiteness theorem states that every unital prime PI-algebra (i.e. a central order in a matrix algebra by Posner's theorem) embeds into a finitely generated module over its center. An analogue of this theorem for alternative and Jordan algebras was earlier proved by V.N.Zhelyabin and the author. In this paper we discuss this problem for associative, classical Jordan and some alternative superalgebras.