Primitive superalgebras with superinvolution. (English) Zbl 0915.16036

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.
Reviewer: V.Drensky (Sofia)


16W55 “Super” (or “skew”) structure
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16P20 Artinian rings and modules (associative rings and algebras)
16K20 Finite-dimensional division rings
16S50 Endomorphism rings; matrix rings
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
17A70 Superalgebras
17C70 Super structures
Full Text: DOI


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