Primitive Superalgebras with Superinvolution

Abstract

Our main purpose is to provide for primitive associative superalgebras a structure theory analogous to that for algebras [5,6,10] and to classify primitive superrings with superinvolution having a minimal one-sided superideal. We were led to this problem by our work on finite dimensional central simple Jordan superalgebras over fields of characteristic not 2 [9] (see also [7]). Of course, just as symmetric elements give rise to Jordan superalgebras, skewsymmetric elements give rise to Lie superalgebras [8,4]. The results and methods are closely related to those of structure theory of associative rings and central simple associative algebras with involution [5, Chap. I;6, Chaps. II, III;1, Chap. X;10, Chap. 2]. Some of the results have been announced in [13].