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International Journal of Mathematics and Mathematical Sciences
Volume 25, Issue 8, Pages 509-516

Algebraic and categorical properties of r-ideal systems

Department of Mathematics, University of Patras, Patras 26500, Greece

Received 19 April 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The structures (G,r), where r is a system of ideals defined on a directed group G, play an important role in solving arithmetical problems. In this paper, we investigate how some properties of these systems are transferred in their cartesian products and their substructures. The results we obtain find an application in the study of categorical properties of these structures.