International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 76951, 9 pages

Minimal conditions on Clifford semigroup congruences

M. El-Ghali M. Abdallah, L. N. Gab-Alla, and Sayed K. M. Elagan

Department of Mathematics, Faculty of Science, Menoufiya University, Shebin El-kom 32511, Egypt

Received 6 April 2006; Accepted 6 April 2006

Copyright © 2006 M. El-Ghali M. Abdallah 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.


A known result in groups concerning the inheritance of minimal conditions on normal subgroups by subgroups with finite indexes is extended to semilattices of groups [E(S),Se,ϕe,f] with identities in which all ϕe,f are epimorphisms (called q partial groups). Formulation of this result in terms of q congruences is also obtained.