International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 71, Pages 4465-4471
doi:10.1155/S0161171203210693
Nagata rings and directed unions of Artinian subrings
Department of Mathematics, Faculty of Sciences Semlalia, University of Cadi Ayyad, P.O. Box 2390, Marrakech, Morocco
Received 24 October 2002
Copyright © 2003 D. Karim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We investigate when a Nagata ring R(X) can be written as a directed union of Artinian subrings. For a family of zero-dimensional rings {Rα}α∈A, we show that ∏α∈ARα(Xα) is not a directed sum of Artinian subrings.