  We study just infinite algebras which remain so upon extension of scalars by
arbitrary field extensions. Such rings are called stably just infinite. We show
that just infinite rings over algebraically closed fields are stably just
infinite provided that the ring is either right noetherian or countably
generated over a large field. We give examples to show that, over countable
fields, a just infinite algebra which is either affine or non-noetherian need
not remain just infinite under extension of scalars. We also give a concrete
classification of PI stably just infinite rings and give two characterizations
of non-PI stably just infinite rings in terms of Martindale's extended center.
