Geodesic
The maximal subsemigroups of the ideals of some semigroups of partial injections
Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 2, pp. 153-167.

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We study the structure of the ideals of the semigroup IO_n of all isotone (order-preserving) partial injections as well as of the semigroup IM_n of all monotone (order-preserving or order-reversing) partial injections on an n-element set. The main result is the characterization of the maximal subsemigroups of the ideals of IO_n and IM_n.
Keywords: finite transformation semigroup, isotone and monotone partial transformations, maximal subsemigroups 
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Dimitrova, Ilinka; Koppitz, Jörg. The maximal subsemigroups of the ideals of some semigroups of partial injections. Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 2, pp. 153-167. http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a3/

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