The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain

Dimitrova, Ilinka; Fernandes, Vítor H.; Koppitz, Jörg

doi:10.5486/pmd.2012.4897

Cited by 14 publications

(9 citation statements)

References 12 publications

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“…The maximal subsemigroups of several of the monoids considered in this section have been described in the literature. The maximal subsemigroups of OP n and OR n were described in [12], those of POI n were found in [24], and those of PODI n were found in [13]. The maximal subsemigroups of the singular ideal of O n were found in [11], and those of the singular ideal of PO n in [14].…”

Section: Partial Transformation Monoidsmentioning

confidence: 96%

“…The maximal subsemigroups of OP n and OR n were originally described in [12]. We restate these results in the following theorems.…”

Section: Op N and Or Nmentioning

confidence: 99%

“…Having defined these notions, we can introduce the twelve monoids of partial transformations that we consider here. These monoids have been extensively studied, see [12,14] and the references therein, where the notation used in this paper originates.…”

Section: Partial Transformation Monoids -Definitionsmentioning

confidence: 99%

“…Lemma 2. 12. If G acts transitively on the L -classes of J, then no maximal subsemigroups of types (M2) or (M3) arise from J.…”

Section: 21mentioning

confidence: 99%

“…Hence there are no maximal subsemigroups of types (M2), (M3), or (M4) arising from J, by Lemma 2. 12. By Proposition 2.7, it remains to describe the maximal subsemigroups of type (M5).…”

Section: Maximal Subsemigroups That Intersect Every H -Class: Type (M5)mentioning

confidence: 99%

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Maximal subsemigroups of finite transformation and diagram monoids

et al. 2018

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We describe and count the maximal subsemigroups of many well-known monoids of transformations and monoids of partitions. More precisely, we find the maximal subsemigroups of the full spectrum of monoids of order-or orientationpreserving transformations and partial permutations considered by V. H. Fernandes and co-authors (12 monoids in total); the partition, Brauer, Jones, and Motzkin monoids; and certain further monoids.Although descriptions of the maximal subsemigroups of some of the aforementioned classes of monoids appear in the literature, we present a unified framework for determining these maximal subsemigroups. This approach is based on a specialised version of an algorithm for determining the maximal subsemigroups of any finite semigroup, developed by the third and fourth authors. This allows us to concisely present the descriptions of the maximal subsemigroups, and to more clearly see their common features.

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Section: Partial Transformation Monoidsmentioning

confidence: 96%

“…The maximal subsemigroups of OP n and OR n were originally described in [12]. We restate these results in the following theorems.…”

Section: Op N and Or Nmentioning

confidence: 99%

Section: Partial Transformation Monoids -Definitionsmentioning

confidence: 99%

“…Lemma 2. 12. If G acts transitively on the L -classes of J, then no maximal subsemigroups of types (M2) or (M3) arise from J.…”

Section: 21mentioning

confidence: 99%

“…Hence there are no maximal subsemigroups of types (M2), (M3), or (M4) arising from J, by Lemma 2. 12. By Proposition 2.7, it remains to describe the maximal subsemigroups of type (M5).…”

Section: Maximal Subsemigroups That Intersect Every H -Class: Type (M5)mentioning

confidence: 99%

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