2007/03/26 by Jason P. Bell, Jason Bell, Bell, Jason +4
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.RA #msc:16N60 #msc:16P40
paper · pdf · doi:10.48550/arxiv.math/0703774
fixed typos
arxiv created 2007/06/22 · arxiv updated 2009/12/01
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.