Nagata rings and directed unions of Artinian subrings
D. Karim1
Received24 Oct 2002
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.