Abstract
The purpose of this paper is to determine all posetsP such that the monoid of all order-preserving maps ofP intoP is regular in the semigroup-theoretic sense.
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References
A. H. Clifford and G. B. Preston (1961)The Algebraic Theory of Semigroups, Vol. 1, Amer. Math. Soc., Providence, R.I.
Proceedings of a Symposium on Regular Semigroups (1979) Northern Illinois University, DeKalb, Ill.
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Communicated by K. Keimel
AMS subject classifications (1980). 06A10, 20M20.
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Adams, M.E., Gould, M. Posets whose monoids of order-preserving maps are regular. Order 6, 195–201 (1989). https://doi.org/10.1007/BF02034336
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DOI: https://doi.org/10.1007/BF02034336