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MAXIMAL PROPERTIES OF SOME SUBSEMIBANDS OF ORDER-PRESERVING FULL TRANSFORMATIONS

  • Zhao, Ping ;
  • Yang, Mei
  • Received : 2011.12.12
  • Published : 2013.03.31

Abstract

Let [$n$] = {1, 2, ${\ldots}$, $n$} be ordered in the standard way. The order-preserving full transformation semigroup ${\mathcal{O}}_n$ is the set of all order-preserving singular full transformations on [$n$] under composition. For this semigroup we describe maximal subsemibands, maximal regular subsemibands, locally maximal regular subsemibands, and completely obtain their classification.

Keywords

order-preserving full transformation semigroup;maximal subsemiband;maximal regular subsemiband;locally maximal subsemiband;locally maximal regular subsemiband

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Cited by

  1. On the semigroups of order-preserving transformations generated by idempotents of rank n −1 vol.16, pp.02, 2017, https://doi.org/10.1142/S0219498817500232
  2. Maximal Regular Subsemibands of the Finite Order-Preserving Partial Transformation Semigroups $$\mathcal {PO}(n,r)$$ PO ( n , r ) vol.40, pp.3, 2017, https://doi.org/10.1007/s40840-016-0344-0
  3. Locally maximal regular subsemibands of the finite transformation semigroups $${\mathcal {T}}(n,r)$$T(n,r) pp.1432-2137, 2018, https://doi.org/10.1007/s00233-018-9981-y

Acknowledgement

Supported by : Natural Science Fund of Guizhou