Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MAXIMAL PROPERTIES OF SOME SUBSEMIBANDS OF ORDER-PRESERVING FULL TRANSFORMATIONS

  • Zhao, Ping (School of Mathematics and Computer Science GuiZhou Normal University / Mathematics Teaching & Research Section Guiyang Medical College) ;
  • Yang, Mei (Cadre Proppants)
  • Received : 2011.12.12
  • Published : 2013.03.31
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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

Acknowledgement

Supported by : Natural Science Fund of Guizhou

References

  1. A. Ya. Aizenstat, The defining relations of the endomorphism semigroup of a finite linearly ordered set, Sibirsk. Mat. 3 (1962), 161-169.
  2. G. U. Garba, On the idempotent ranks of certain semigroups of order-preserving transformations, Portugal. Math. 51 (1994), no. 2, 185-204.
  3. G. M. S. Gomes and J. M. Howie, On the ranks of certain semigroups of order-preserving transformations, Semigroup Forum 45 (1992), no. 3, 272-282. https://doi.org/10.1007/BF03025769
  4. P. M. Higgins, Idempotent depths in semigroups of order-preserving mappings, Proc. Roy. Soc. Edinburgh Sect. A 124 (1994), no. 5, 1045-1058. https://doi.org/10.1017/S0308210500022502
  5. J. M. Howie, Products of idempotents in certain semigroups of transformation, Proc. Edinburgh Math. Soc. 17 (1971), 223-236. https://doi.org/10.1017/S0013091500026936
  6. A. Laradji and A. Umar, Combinatorial results for semigroups of order-preserving full transformations, Semigroup Forum 62 (2006), no. 1, 51-62.
  7. F. Pastijin, Embedding semigroups in semibands, Semigroup Forum 14 (1977), no. 3, 247-263. https://doi.org/10.1007/BF02194670
  8. A. Umar, On the semigroups of order-decreasing finite full transformations, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), no. 1-2, 129-142. https://doi.org/10.1017/S0308210500015031
  9. B. Xu, P. Zhao, and J. Y. Li, Locally maximal idempotent-generated subsemigroups of singular order-preserving transformation semigroups, Semigroup Forum 72 (2006), no. 3, 488-492. https://doi.org/10.1007/s00233-005-0551-8
  10. X. L. Yang, On the nilpotent ranks of the principal factors of order-preserving transfor-mation semigroups, Semigroup Forum 57 (1998), no. 3, 331-340. https://doi.org/10.1007/PL00005983
  11. X. L. Yang, Products of idempotents of defect 1 in certain semigroups of transformations, Comm. Algebra 27 (1999), no. 7, 3557-3568. https://doi.org/10.1080/00927879908826646
  12. X. L. Yang and C. H. Lu, Maximal properties of some subsemigroups in finite order-preserving transformation semigroups, Comm. Algebra 28 (2000), no. 7, 3125-3135. https://doi.org/10.1080/00927870008827014
  13. P. Zhao, B. Xu, and M. Yang, A note on maximal properties of some subsemigroups of order-preserving transformation semigroups, Comm. Algebra 40 (2012), no. 3, 1116-1121. https://doi.org/10.1080/00927872.2010.546002

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