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International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 794013, 11 pages
http://dx.doi.org/10.1155/2008/794013
Research Article

Regularity and Green's Relations on a Semigroup of Transformations with Restricted Range

1Department of Mathematics, Chiang Mai University, Chiangmai 50200, Thailand
2Department of Mathematics, Chiangmai Rajabhat University, Chiangmai 50300, Thailand

Received 14 May 2008; Accepted 18 September 2008

Academic Editor: Robert Redfield

Copyright © 2008 Jintana Sanwong and Worachead Sommanee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [14 citations]

The following is the list of published articles that have cited the current article.

  • Jintana Sanwong, “The regular part of a semigroup of transformations with restricted range,” Semigroup Forum, vol. 83, no. 1, pp. 134–146, 2011. View at Publisher · View at Google Scholar
  • Suzana Mendes-Goncalves, and R. P. Sullivan, “The Ideal Structure Of Semigroups Of Transformations With Restricted Range,” Bulletin of The Australian Mathematical Society, vol. 83, no. 2, pp. 289–300, 2011. View at Publisher · View at Google Scholar
  • Kritsada Sangkhanan, and Jintana Sanwong, “Partial Orders On Semigroups Of Partial Transformations With Restricted Range,” Bulletin of the Australian Mathematical Society, vol. 86, no. 01, pp. 100–118, 2012. View at Publisher · View at Google Scholar
  • Lei Sun, “A note on abundance of certain semigroups of transformations with restricted range,” Semigroup Forum, 2013. View at Publisher · View at Google Scholar
  • Worachead Sommanee, and Jintana Sanwong, “Rank and idempotent rank of finite full transformation semigroups with restricted range,” Semigroup Forum, vol. 87, no. 1, pp. 230–242, 2013. View at Publisher · View at Google Scholar
  • Vítor H. Fernandes, and Jintana Sanwong, “On the Ranks of Semigroups of Transformations on a Finite Set with Restricted Range,” Algebra Colloquium, vol. 21, no. 03, pp. 497–510, 2014. View at Publisher · View at Google Scholar
  • Vitor H. Fernandes, Preeyanuch Honyam, Teresa M. Quinteiro, and Boorapa Singha, “On semigroups of endomorphisms of a chain with restricted range,” Semigroup Forum, vol. 89, no. 1, pp. 77–104, 2014. View at Publisher · View at Google Scholar
  • Worachead Sommanee, and Jintana Sanwong, “Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals,” Algebra universalis, 2015. View at Publisher · View at Google Scholar
  • Bernd Billhardt, Ekkachai Laysirikul, Kritsada Sangkhanan, Jintana Sanwong, and Worachead Sommanee, “On $$\mathcal {R}$$ R -unipotent semigroups with $$\Pi L^1$$ Π L 1 -embeddable band of idempotents,” Semigroup Forum, 2015. View at Publisher · View at Google Scholar
  • Igor Dolinka, and James East, “Variants of finite full transformation semigroups,” International Journal of Algebra and Computation, pp. 1550037, 2015. View at Publisher · View at Google Scholar
  • Lei Sun, and Junling Sun, “A natural partial order on certain semigroups of transformations with restricted range,” Semigroup Forum, 2015. View at Publisher · View at Google Scholar
  • Vítor H. Fernandes, Preeyanuch Honyam, Teresa M. Quinteiro, and Boorapa Singha, “On Semigroups of Orientation-preserving Transformations with Restricted Range,” Communications in Algebra, vol. 44, no. 1, pp. 253–264, 2016. View at Publisher · View at Google Scholar
  • Jittisak Rakbud, and Pattama Purisang, “Regularity of transformation semigroups defined by a partition,” Communications of the Korean Mathematical Society, vol. 31, no. 2, pp. 217–227, 2016. View at Publisher · View at Google Scholar
  • Bernd Billhardt, Yanisa Chaiya, Ekkachai Laysirikul, Kritsada Sangkhanan, and Jintana Sanwong, “ On left quasi-ample semigroups with Π L 1 -embeddable band of idempotents ,” Communications in Algebra, pp. 1–11, 2017. View at Publisher · View at Google Scholar