Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 2, pp. 467-470 (2003)

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Zero-dimensional pairs

Driss Karim

Department of Mathematics, Faculty of Sciences Semlalia, P. O. Box 2390 Marrakech, Morocco, e-mail:

Abstract: If $\{(R_{i},T_{i})\}_{i=1}^{n}$ is a finite family of zero-dimensional pairs, then $(\prod_{i=1}^{n}R_{i},\prod_{i=1}^{n}T_{i})$ is zero-dimensional pair but this result fails for an infinite family of zero-dimensional 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 zero-dimensional pairs $\{(R_{\alpha},T_{\alpha})\}_{\alpha\in A}$ is zero-dimensional pair.

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Electronic version published on: 1 Aug 2003. This page was last modified: 4 May 2006.

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