Dimitrova, Ilinka; Koppitz, Jörg The maximal subsemigroups of the ideals of some semigroups of partial injections. (English) Zbl 1198.20054 Discuss. Math., Gen. Algebra Appl. 29, No. 2, 153-167 (2009). 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 \(IM_n\). Cited in 1 ReviewCited in 6 Documents MSC: 20M20 Semigroups of transformations, relations, partitions, etc. 20M12 Ideal theory for semigroups Keywords:ideals; semigroups of isotone partial injections; semigroups of monotone partial injections; maximal subsemigroups; finite transformation semigroups PDFBibTeX XMLCite \textit{I. Dimitrova} and \textit{J. Koppitz}, Discuss. Math., Gen. Algebra Appl. 29, No. 2, 153--167 (2009; Zbl 1198.20054) Full Text: DOI Link