Central orders in simple finite dimensional superalgebras

TL;DR

This paper extends the concept of central orders and module finiteness theorems to associative, classical Jordan, and some alternative superalgebras, broadening the scope of classical algebraic results.

Contribution

It generalizes Formanek's module finiteness theorem to superalgebras, including associative, Jordan, and certain alternative types.

Findings

Established analogues of the finiteness theorem for superalgebras.

Demonstrated embeddings of superalgebras into finitely generated modules over their centers.

Extended classical algebraic results to the superalgebra context.

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.