REGULARITY OF TRANSFORMATION SEMIGROUPS DEFINED BY A PARTITION

- Journal title : Communications of the Korean Mathematical Society
- Volume 31, Issue 2, 2016, pp.217-227
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2016.31.2.217

Title & Authors

REGULARITY OF TRANSFORMATION SEMIGROUPS DEFINED BY A PARTITION

Purisang, Pattama; Rakbud, Jittisak;

Purisang, Pattama; Rakbud, Jittisak;

Abstract

Let X be a nonempty set, and let $\mathfrak{F}

Keywords

full transformation semigroup;regular element;character;

Language

English

References

1.

R. Chinram, Green's relations and regularity of generalized semigroups of linear transformations, Lobachevskii J. Math. 30 (2009), no. 4, 253-256.

2.

A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, RI, USA, 1961.

3.

A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. Vol. II, Mathematical Surveys, No. 7, American Mathematical Society, Providence, RI, USA, 1967.

4.

L.-Z. Deng, J.-W. Zeng, and B. Xu, Green's relations and regularity for semigroups of transformations that preserve double direction equivalence, Semigroup Forum 80 (2010), no. 3, 416-425.

5.

P. Honyam and J. Sanwong, Semigroups of transformations with invariant set, J. Korean Math. Soc. 48 (2011), no. 2, 289-300.

6.

P. Honyam and J. Sanwong, Semigroups of linear transformations with invariant subspaces, Int. J. Algebra 6 (2012), no. 8, 375-386.

7.

Y. Kemprasit and T. Changphas, Regular order-preserving transformation semigroups, Bull. Austral. Math. Soc. 62 (2000), no. 3, 511-524.

8.

S. Lei and P. Huisheng, Green's relations on semigroups of transformations preserving two equivalence relations, J. Math. Res. Exposition 29 (2009), no. 3, 415-422.

9.

W. Mora and Y. Kemprasit, Regular elements of some order-preserving transformation semigroups, Int. J. Algebra 4 (2010), no. 13, 631-641.

10.

S. Nenthein, P. Youngkhong, and Y. Kemprasit, Regular elements of some transformation semigroups, Pure Math. Appl. 16 (2005), no. 3, 307-314.

11.

H. Pei, Equivalences, ${\alpha}$ -semigroups and ${\alpha}$ -congruences, Semigroup Forum 49 (1994), no. 1, 49-58.

12.

H. Pei, Regularity and Green's relations for semigroups of transformations that preserve an equivalence, Commun. Algebra 33 (2005), no. 1, 109-118.

13.

H. Pei, A note on semigroups of linear transformations with invariant subspaces, Int. J. Algebra 6 (2012), no. 27, 1319-1324.

14.

H. Pei and D. Zou, Green's equivalences on semigroups of transformations preserving order and an equivalence relation, Semigroup Forum 71 (2005), no. 2, 241-251.

15.

J. Sanwong, The regular part of a semigroup of transformations with restricted range, Semigroup Forum 83 (2011), no. 1, 134-146.

16.

J. Sanwong and W. Sommanee, Regularity and Green's relations on a semigroup of transformations with restricted range, Int. J. Math. Math. Sci. 2008 (2008), Article ID 794013, 11 pages.

17.

R. P. Sullivan, Semigroups of linear transformations with restricted range, Bull. Austral. Math. Soc. 77 (2008), no. 3, 441-453.