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.
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机译：令X为非空集。对于X的固定子集Y，令F i x X，Y为X上所有固定了Y中所有元素的自映射的集合。那么F i x X，Y在映射的组成下是一个正则半定式。在本文中，我们表征了F i x（X，Y）上的自然偏序，并且该结果扩展了由于Kowol和Mitsch而导致的结果。此外，我们找到了兼容的元素，并描述了最小和最大元素。
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