We study the structure of the semigroup OT n , which is a unique (up to an isomorphism) R-section of the semigroup T n . For this semigroup, we describe Green relations, determine regular and nilpotent elements, describe maximal nilpotent subsemigroups, and determine the unique irreducible system of generatrices and maximal subsemigroups.
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V. Pyekhtyeryev, “H- and R-cross-sections of the full finite semigroup T n ,” J. Alg. Discr. Math., No. 3, 82–88 (2003).
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. 1, American Mathematical Society, Providence, RI (1964).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 9, pp. 1240–1246, September, 2009.
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Pekhterev, V.O. Structure of the semigroup OT n . Ukr Math J 61, 1467–1474 (2009). https://doi.org/10.1007/s11253-010-0289-7
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DOI: https://doi.org/10.1007/s11253-010-0289-7