Stably Just Infinite Rings

Details Stably Just Infinite Rings Stably Just Infinite Rings

2007-03-26

arxiv.org/abs/math/0703774v3

Mathematics

Rings and Algebras

fixed typos

Scientific paper

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.

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