International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 984274 | https://doi.org/10.1155/S016117120430150X

Niovi Kehayopulu, "Ideal extensions of ordered sets", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 984274, 15 pages, 2004. https://doi.org/10.1155/S016117120430150X

Ideal extensions of ordered sets

Received30 Jan 2003

Abstract

The ideal extensions of semigroups—without order—have been first considered by Clifford (1950). In this paper, we give the main theorem of the ideal extensions for ordered sets. If P, Q are disjoint ordered sets, we construct (all) the ordered sets V which have an ideal P which is isomorphic to P, and the complement of P in V is isomorphic to Q. Conversely, we prove that every extension of an ordered set P by an ordered set Q can be so constructed. Illustrative examples of the main theorem in case of finite ordered sets are given.

Copyright © 2004 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.


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