Examples of Pomonoids of Full Transformations of a Poset

(Bana Al Subaiei)

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Abstract

In this research, the partially ordered monoid (simple pomonoid) full transformations of a poset O(X) is studied, and some related properties are examined. We show that when the poset X_  is not totally ordered, the pomonoid of all decreasing singular self-maps of a poset X_ (denoted by S^-) and the pomonoid of all increasing singular self-maps of a poset X_  (denoted by S^+) may not be generally isomorphic. Some specific partial ordered relations are considered, and the cardinalities of S^- and S^+ under these relations are found. The set of fixed, decreasing, and increasing points of mapping α in O(X) are also investigated.


KEYWORDS
Posets, pomonoids, full transformations
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References

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