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The maximal subsemigroups of the ideals of some semigroups of partial injections. (English) Zbl 1198.20054

Summary: 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 \(IM_n\).

MSC:

20M20 Semigroups of transformations, relations, partitions, etc.
20M12 Ideal theory for semigroups
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