Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 44, No. 2, pp. 467470 (2003) 

Zerodimensional pairsDriss KarimDepartment of Mathematics, Faculty of Sciences Semlalia, P. O. Box 2390 Marrakech, Morocco, email: ikarim@ucam.ac.maAbstract: If $\{(R_{i},T_{i})\}_{i=1}^{n}$ is a finite family of zerodimensional pairs, then $(\prod_{i=1}^{n}R_{i},\prod_{i=1}^{n}T_{i})$ is zerodimensional pair but this result fails for an infinite family of zerodimensional pairs. We give necessary and sufficient conditions in order that an infinite product $(\prod_{\alpha\in A}R_{\alpha},\prod_{\alpha\in A }T_{\alpha})$ of zerodimensional pairs $\{(R_{\alpha},T_{\alpha})\}_{\alpha\in A}$ is zerodimensional pair. Full text of the article:
Electronic version published on: 1 Aug 2003. This page was last modified: 4 May 2006.
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