Kyungpook Mathematical Journal

  • 제58권4호
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  • Pages.627-635
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  • 2018
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Regularity of a Particular Subsemigroup of the Semigroup of Transformations Preserving an Equivalence

  • Rakbud, Jittisak (Department of Mathematics, Faculty of Science, Silpakorn University)
  • 투고 : 2018.07.26
  • 심사 : 2018.10.24
  • 발행 : 2018.12.23
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초록

In this paper, we use the notion of characters of transformations provided in [8] by Purisang and Rakbud to define a notion of weak regularity of transformations on an arbitrarily fixed set X. The regularity of a semigroup of weakly regular transformations on a set X is also investigated.

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참고문헌

  1. J. Araujo and J. Konieczny Semigroups of transformations preserving an equivalence relation and a cross-section, Commun. Algebra, 32(5)(2004), 1917-1935. https://doi.org/10.1081/AGB-120029913
  2. V. H. Fernandes, P. Honyam, T. M. Quinteiro, and B.Singha, On semigroups of orientation-preserving transformations with restricted range, Comm. Algebra, 44(1)(2016), 253-264. https://doi.org/10.1080/00927872.2014.975345
  3. P. Honyam and J. Sanwong, Semigroups of transformations with invariant set, J. Korean Math. Soc., 48(2)(2011), 289-300. https://doi.org/10.4134/JKMS.2011.48.2.289
  4. P. Huisheng, Equivalences, ${\alpha}$-semigroups and ${\alpha}$-congruences, Semigroup Forum, 49(1)(1994), 49-58. https://doi.org/10.1007/BF02573470
  5. P. Huisheng, Regularity and Green's relations for semigroups of transformations that preserve an equivalence, Commun. Algebra, 33(1)(2005), 109-118. https://doi.org/10.1081/AGB-200040921
  6. P. Huisheng and Z. Dingyu Green's equivalences on semigroups of transformations preserving order and an equivalence relation, Semigroup Forum, 71(2)(2005), 241-251. https://doi.org/10.1007/s00233-005-0514-0
  7. S. Nenthein, P. Youngkhong and Y. Kemprasit, Regular of elements of some transformation semigroups, Pure Math. Appl., 16(3)(2005), 307-314.
  8. P. Purisang and J. Rakbud, Regularity of transformation semigroups defined by a partition, Commun. Korean Math. Soc., 31(2)(2016), 217-227. https://doi.org/10.4134/CKMS.2016.31.2.217
  9. J. Sanwong, The regular part of a semigroup of transformations with restricted range, Semigroup Forum, 83(1)(2011), 134-146. https://doi.org/10.1007/s00233-011-9320-z
  10. J. Sanwong and W. Sommanee, Regularity and Green's relations on a semigroup of transformations with restricted range, Int. J. Math. Math. Sci., (2008), Art. ID 794013, 11 pp.
  11. K. Tinpun and J. Koppitz, Relative rank of the finite full transformation semigroup with restricted range, Acta Math. Univ. Comenian., 85(2)(2016), 347-356.