Abstract
A partial transformation α on an n-element chain X n is called order-preserving if x ≤ y implies xα ≤yα for all x, y in the domain of α and it is called extensive if x ≤ xα for all x in the domain of α. The set of all partial order-preserving extensive transformations on X n forms a semiband POE n . We determine the maximal subsemigroups as well as the maximal subsemibands of POE n .
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The authors thanks the referee of this article for their numerous valuable suggestions.
This work was supported by SWU-Blagoevgrad Research Project NID-N9/F-7 for the first author and by DFG Research Project GZ: KO 1546/3-1 for the second author.
Notes
Communicated by V. Gould.