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]].
