Natural Partial Orders on Transformation Semigroups with Fixed Sets - Yanisa Chaiya (2018)
© 2016 Yanisa Chaiya et al. Let X be a nonempty set. For a fixed subset Y of X, let Fix(X, Y) be the set of all self-maps on X which fix all elements in Y. Then Fix(X, Y) is a regular monoid under the composition of maps. In this paper, we characterize the natural partial order on Fix(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.