Central orders in simple finite dimensional superalgebras (Q2200983)

A well known theorem of \textit{E. Formanek} [Commun. Algebra 1, 79--86 (1974; Zbl 0272.16004)] states that every prime PI algebra can be embedded into a finitely generated module over its centre. Similar results were obtained by \textit{A. S. Panasenko} [Math. Notes 98, No. 5, 805--812 (2015; Zbl 1360.17035); translation from Mat. Zametki 98, No. 5, 747--755 (2015)] for alternative prime non-degenerate algebras, and by \textit{V. N. Zhelyabin} and \textit{A. S. Panasenko} [Algebra Logic 57, No. 5, 336--352 (2018; Zbl 1441.17024); translation from Algebra Logika 57, No. 5, 522--546 (2018)], for central orders in finite dimensional simple Jordan algebras. The author studies an analogous problem for central orders in finite dimensional simple associative, alternative, and Jordan superalgebras. In the associative case Formanek's theorem holds for superalgebras while in the case of alternative and Jordan superalgebras additional restrictions must be imposed.