On Epiorthodox Semigroups
It has been well known that the band of idempotents of a naturally ordered orthodox semigroup satisfying the “strong Dubreil-Jacotin condition” forms a normal band. In the literature, the naturally ordered orthodox semigroups satisfying the strong Dubreil-Jacotin condition were first considered by...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/181707 |
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| author | Shouxu Du Xinzhai Xu K. P. Shum |
| author_facet | Shouxu Du Xinzhai Xu K. P. Shum |
| author_sort | Shouxu Du |
| collection | DOAJ |
| description | It has been well known that the band of idempotents of a naturally
ordered orthodox semigroup satisfying the “strong Dubreil-Jacotin condition” forms a normal band. In the literature, the naturally ordered orthodox semigroups satisfying the strong Dubreil-Jacotin condition were first considered by Blyth and Almeida Santos in 1992. Based on the name “epigroup” in the paper of Blyth and Almeida Santos and also the name “epigroups” proposed by Shevrin in 1955; we now call the naturally ordered orthodox semigroups satisfying the Dubreil-Jacotin condition
the epiorthodox semigroups. Because the structure of this kind of orthodox
semigroups has not yet been described, we therefore give a structure theorem
for the epi-orthodox semigroups. |
| format | Article |
| id | doaj-art-cc28c95eec194c5f839aebd7a7d40967 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cc28c95eec194c5f839aebd7a7d409672025-02-03T06:07:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/181707181707On Epiorthodox SemigroupsShouxu Du0Xinzhai Xu1K. P. Shum2Department of Basic Science, Qingdao Binhai University, Qingdao, Shandong 266555, ChinaCollege of Mathematics Science, Shandong Normal University, Jinan, Shandong 250014, ChinaThe Institute of Mathematics, Yunnan University, Kunming 650091, ChinaIt has been well known that the band of idempotents of a naturally ordered orthodox semigroup satisfying the “strong Dubreil-Jacotin condition” forms a normal band. In the literature, the naturally ordered orthodox semigroups satisfying the strong Dubreil-Jacotin condition were first considered by Blyth and Almeida Santos in 1992. Based on the name “epigroup” in the paper of Blyth and Almeida Santos and also the name “epigroups” proposed by Shevrin in 1955; we now call the naturally ordered orthodox semigroups satisfying the Dubreil-Jacotin condition the epiorthodox semigroups. Because the structure of this kind of orthodox semigroups has not yet been described, we therefore give a structure theorem for the epi-orthodox semigroups.http://dx.doi.org/10.1155/2011/181707 |
| spellingShingle | Shouxu Du Xinzhai Xu K. P. Shum On Epiorthodox Semigroups International Journal of Mathematics and Mathematical Sciences |
| title | On Epiorthodox Semigroups |
| title_full | On Epiorthodox Semigroups |
| title_fullStr | On Epiorthodox Semigroups |
| title_full_unstemmed | On Epiorthodox Semigroups |
| title_short | On Epiorthodox Semigroups |
| title_sort | on epiorthodox semigroups |
| url | http://dx.doi.org/10.1155/2011/181707 |
| work_keys_str_mv | AT shouxudu onepiorthodoxsemigroups AT xinzhaixu onepiorthodoxsemigroups AT kpshum onepiorthodoxsemigroups |