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Abstract
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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

D. Karim

Department of Mathematics, Faculty of Sciences Semlalia, University of Cadi Ayyad, P.O. Box 2390, Marrakech, Morocco

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.