On Semigroups of Orientation-preserving Transformations with Restricted Range

REFERENCES

• Araújo , J. , Fernandes , V. H. , Jesus , M. M. , Maltcev , V. , Mitchell , J. D. ( 2011 ). Automorphisms of partial endomorphism semigroups . Publicationes Mathematicae Debrecen 79 ( 1–2 ): 23 – 39 .
   Web of Science ®Google Scholar
• Arthur , R. E. , Ruškuc , N. ( 2000 ). Presentations for two extensions of the monoid of order-preserving mappings on a finite chain . Southeast Asian Bull. Math. 24 : 1 – 7 .
   Google Scholar
• Catarino , P. M. ( 1998 ). Monoids of orientation-preserving transformations of a finite chain and their presentations. Proc. of the Conference in St. Andrews, Scotland 1997, pp. 39–46 .
   Google Scholar
• Catarino , P. M. , Higgins , P. M. ( 1999 ). The monoid of orientation-preserving mappings on a chain . Semigroup Forum 58 : 190 – 206 .
   Web of Science ®Google Scholar
• Dimitrova , I. , Fernandes , V. H. , Koppitz , J. (2012). The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain. Publicationes Mathematicae Debrecen 81(1–2):11–29.
   Web of Science ®Google Scholar
• Fernandes , V. H. , Gomes , G. M. S. , Jesus , M. M. ( 2009 ). Congruences on monoids of transformation preserving the orientation on a finite chain . J. Algebra 321 : 743 – 757 .
   Web of Science ®Google Scholar
• Fernandes , V. H. , Gomes , G. M. S. , Jesus , M. M. ( 2011 ). The cardinal and the idempotent number of various monoids of transformations on a finite chain . Bulletin of the Malaysian Mathematical Sciences Society 34 ( 2 ): 79 – 85 .
   Google Scholar
• Fernandes , V. H. , Honyam , P. , Quinteiro , T. M. , Singha , B. ( 2014 ). On semigroups of endomorphisms of a chain with restricted range . Semigroup Forum 89 ( 1 ): 77 – 104 .
   Web of Science ®Google Scholar
• Fernandes , V. H. , Quinteiro , T. M. ( 2011 ). Bilateral semidirect product decompositions of transformation monoids . Semigroup Forum 82 : 271 – 287 .
   Web of Science ®Google Scholar
• Fernandes , V. H. , Quinteiro , T. M. ( 2012 ). The cardinal of various monoids of transformations that preserve a uniform partition . Bulletin of the Malaysian Mathematical Sciences Society 35 ( 4 ): 885 – 896 .
   Web of Science ®Google Scholar
• Fernandes , V. H. , Quinteiro , T. M. ( 2014 ). On the ranks of certain monoids of transformations that preserve a uniform partition . Communications in Algebra 42 : 615 – 636 .
   Web of Science ®Google Scholar
• Fernandes , V. H. , Sanwong , J. ( 2014 ). On the rank of semigroups of transformations on a finite set with restricted range . Algebra Colloq. 21 : 497 – 510 .
   Web of Science ®Google Scholar
• Gould , H. W. ( 1972 ). Combinatorial Identities, A Standardized Set of Tables Listing 500 Binomial Coefficient Summations . Revised Edition 1972, Published by the author. Printed by Morgantown Printing and Binding Co., Morgantown, W. Va. (3) +viii +106 pp. LC Cat.Card No. 73-179239 .
   Google Scholar
• Howie , J. M. ( 1995 ). Fundamentals of Semigroup Theory . Oxford : Oxford University Press .
   Google Scholar
• Mendes-Gonçalves , S. , Sullivan , R.P. ( 2011 ). The ideal structure of semigroups of transformations with restricted range . Bull. Austral. Math. Soc. 83 : 289 – 300 .
   Web of Science ®Google Scholar
• McAlister , D. B. ( 1998 ). Semigroups generated by a group and an idempotent . Comm. Algebra 26 : 515 – 547 .
   Web of Science ®Google Scholar
• Mora , W. , Kemprasit , Y. ( 2010 ). Regular elements of some order-preserving transformation semigroups . Int. J. Algebra 4 ( 13–16 ): 631 – 641 .
   Google Scholar
• Nenthein , S. , Youngkhong , P. , Kemprasit , Y. ( 2005 ). Regular elements of some transformation semigroups . Pure Math. Appl. 16 ( 3 ): 307 – 314 .
   Google Scholar
• Sanwong , J. , Sommanee , W. ( 2008 ). Regularity and Green's relations on a semigroup of transformations with restricted range . Int. J. Math. Math. Sci. Art. ID 794013, 11 pp .
   Google Scholar
• Sanwong , J. , Singha , B. , Sullivan , R. P. ( 2009 ). Maximal and minimal congruences on some semigroups . Acta Math. Sin. (Engl. Ser.) 25 ( 3 ): 455 – 466 .
   Web of Science ®Google Scholar
• Sullivan , R. P. ( 2008 ). Semigroups of linear transformations with restricted range . Bull. Austral. Math. Soc. 77 : 441 – 453 .
   Web of Science ®Google Scholar
• Symons , J. S. V. ( 1975 ). Some results concerning a transformation semigroup . J. Austral. Math. Soc. 19 : 413 – 425 .
   Google Scholar
• Zhao , P. , Fernandes , V. H. ( 2015 ). The ranks of ideals in various transformation monoids . Communications in Algebra 43 ( 2 ): 674 – 692 .
   Web of Science ®Google Scholar
• Communicated by V. Gould.
   Google Scholar