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 P, Q are disjoint ordered sets, we construct (all) the ordered sets V which have an ideal P′ which is isomorphic to P,...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120430150X |
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| _version_ | 1832553330420744192 |
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| author | Niovi Kehayopulu |
| author_facet | Niovi Kehayopulu |
| author_sort | Niovi Kehayopulu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5aae747676d1407ead54253f81deff0d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5aae747676d1407ead54253f81deff0d2025-02-03T05:54:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004532847286110.1155/S016117120430150XIdeal extensions of ordered setsNiovi Kehayopulu0Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, GreeceThe 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.http://dx.doi.org/10.1155/S016117120430150X |
| spellingShingle | Niovi Kehayopulu Ideal extensions of ordered sets International Journal of Mathematics and Mathematical Sciences |
| title | Ideal extensions of ordered sets |
| title_full | Ideal extensions of ordered sets |
| title_fullStr | Ideal extensions of ordered sets |
| title_full_unstemmed | Ideal extensions of ordered sets |
| title_short | Ideal extensions of ordered sets |
| title_sort | ideal extensions of ordered sets |
| url | http://dx.doi.org/10.1155/S016117120430150X |
| work_keys_str_mv | AT niovikehayopulu idealextensionsoforderedsets |