Ideal extensions of ordered sets

Niovi Kehayopulu

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-15

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.

Date: 2004
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2004/984274.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2004/984274.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:984274

DOI: 10.1155/S016117120430150X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().