Local PI theory of Jordan systems
Let \(x\) be an element in a Jordan system (algebra, pair or triple system). When the local algebra at \(x\) is a PI-algebra, the author says that \(x\) is a PI-element. In this paper it is proved that in a nondegenerate Jordan system the set of the PI-elements is an ideal. First the result is shown in the primitive case. Moreover, under the last assumption it is proved that when this ideal is nonzero then it coincides with the socle.
scientific article; zbMATH DE number 1309258
scientific article