STRONGLY PRIME ALTERNATIVE PAIRS WITH MINIMAL INNER IDEALS

In this paper, we use the known classification of the finite capacity simple alternative pairs and the version of the Litoff Theorem far Jor dan pairs to describe all the strongly prime alternative pairs with no nzero socle. We study the inheritance of some properties (primeness, n ondegenerancy,...) when passing from the original alternative pair to the symmetrized pair. Thus, we can apply Jordan theoretical results to the alternative case.