Natural Partial Orders on Transformation Semigroups with Fixed Sets

Abstract EN

Let X be a nonempty set.

For a fixed subset Y of X , let F i x X , Y be the set of all self-maps on X which fix all elements in Y .

Then F i x X , Y is a regular monoid under the composition of maps.

In this paper, we characterize the natural partial order on F i x ( X , Y ) and this result extends the result due to Kowol and Mitsch.

Further, we find elements which are compatible and describe minimal and maximal elements.