Prime ideals of the Burnside ring of a saturated fusion system

In a 1969 article, A. Dress described the prime ideals of the Burnside ring of a finite group G and the inclusion relations between them. One may ask whether similar results exist for the Burnside ring of a saturated fusion system F on a finite p-group S. The present paper answers positively, providing a typology for the prime ideals of A(F) and for those of A(F) (p) as a consequence.