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
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 , are disjoint ordered sets, we construct (all) the ordered sets which have an ideal which is isomorphic to , and the complement of in is isomorphic to . Conversely, we prove that every extension of an ordered set by an ordered set can be so constructed. Illustrative examples of the main theorem in case of finite ordered sets are given.
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