International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 181707, 14 pages
Research Article

On Epiorthodox Semigroups

1Department of Basic Science, Qingdao Binhai University, Qingdao, Shandong 266555, China
2College of Mathematics Science, Shandong Normal University, Jinan, Shandong 250014, China
3The Institute of Mathematics, Yunnan University, Kunming 650091, China

Received 25 December 2010; Accepted 15 April 2011

Academic Editor: Aloys Krieg

Copyright © 2011 Shouxu Du et al. 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.


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.