Abstract
Given \(\{R_{i}\}_{i\in I}\) and \(\{S_{i}\}_{i\in I}\) two families of zero-dimensional rings such that \(R_{i}\subseteq S_{i}\) for each \(i\in I\). This paper deals with the transfer of the notion “being a directed union of Artinian subrings” from \(\prod _{i\in I}R_{i}\) to \(\prod _{i\in I}S_{i}\).
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