Geodesic
On the Semigroup of all Increasing Full Transformations
Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 164-168.

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Let Tn be the full transformation semigroup on an n-element set and let Incn be the subsemigroup of Tn consisting of all increasing transformations. This paper considers some algebraic and rank properties of the semigroup Incn. It is shown that the semi-group Incn is an R-trivial idempotent-generated semigroup. Finally, the maximal subsemigroups of Incn are characterized. *2000 Mathematics Subject Classification: 20M20.
Keywords: Transformation Semigroup, Increasing Transformation, Rank, Idempotent Rank, Maximal Subsemigroup 
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Dimitrova, Ilinka. On the Semigroup of all Increasing Full Transformations. Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 164-168. http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a12/