Primitive superalgebras with superinvolution
The author studies primitive associative superalgebras and develops their structure theory in the spirit of classical structure theory of (ordinary) associative algebras. In particular, he proves a superanalogue of the density theorem, gives a description of the artinian simple superrings as algebras of endomorphisms of a finite dimensional superspace over a division superalgebra and determines the isomorphisms between two artinian simple superrings. He also presents a complete list of central division superalgebras over a field in terms of the (ordinary) central division algebras over the same field. Then the author describes the primitive superrings with a minimal right superideal. An important application is for the case when the primitive superring has a superinvolution which is crucial for the study of finite dimensional central simple Jordan algebras. Another application is the description of simple superrings with superinvolution.
scientific article; zbMATH DE number 1213836