On the Monoid of All Partial Order-Preserving Extensive Transformations

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 .

Key Words:

• Extensive transformation
• Maximal subsemibands
• Maximal subsemigroups
• Rank
• Transformation semigroup

2000 Mathematics Subject Classification:

• 20M20

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.