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Transformational antiatomic characteristic of ordered sets. (English. Russian original) Zbl 0953.06004
Math. Notes 66, No. 1, 89-93 (1999); translation from Mat. Zametki 66, No. 1, 112-119 (1999).
Summary: To any ordered set with a universally maximal element, a semigroup of transformations having some natural properties is assigned that defines the ordered set up to isomorphism. The system of such transformation semigroups is proved to be the minimal element in the set of all defining systems of transformation semigroups with respect to the following ordering: one system precedes another if for each ordered set from the class in question, the semigroup of its transformations belonging to the first system is contained in the semigroup of its transformations from the second system.
06A06 Partial orders, general
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[1] L. M. Gluskin, ”Semigroups of isotonic transformations,”Uspekhi Mat. Nauk [Russian math. Surveys],16, No. 5, 157–162 (1961).
[2] E. S. Ljapin,Semigroups, Amer. Math. Soc., Providence, R.I. (1974).
[3] E. S. Lyapin, ”Some endomorphisms of an ordered set,”Izv. Vyssh. Uchebn. Zaved. Mat [Soviet Math. (Iz. VUZ)], No. 2, 87–94 (1962).
[4] E. S. Lyapin, ”Semigroups of directed maps of ordered sets,”Mat. Sb. [Math. USSR-Sb.],73, No. 4, 161–168 (1967).
[5] E. S. Lyapin, ”Directed endomorphisms of ordered sets,”Sibirsk. Mat. Zh. [Siberian Math. J.],11, No. 1, 217–221 (1970). · Zbl 0208.28902
[6] L. M. Popova, ”Semigroups of partial endomorphisms of a set with a relation,”Sibirsk. Mat. Zh. [Siberian Math. J.],4, No. 2, 309–317 (1963). · Zbl 0214.27001
[7] A. M. Kalmanovich, ”Semigroups of partial endomorphisms of a graph,”Dopovidi Akad. Nauk URSR, No. 2, 141–150 (1963).
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