Geodesic
A note on intra regularity on semigroups of partial transformations with invariant set
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 333-341.

Voir la notice de l'article provenant de la source Library of Science

Let X be any non-empty set and P(X) denote the semigroup (under composition) of partial transformations on a set X. Let Y be a fixed non-empty subset of X and PT(X,Y) = {α∈ P(X) : (domα∩ Y)α⊆ Y}. Then PT(X,Y) is a semigroup consisting of all mapping in P(X) that leave Y ⊆ X invariant. In this paper, we present criteria for checking the intra-regularity of elements in PT(X,Y) and apply these results to quantify intra-regular elements in PT(X,Y), when X is finite.
Keywords: partial transformation semigroup, intra regularity, invariant set 
@article{DMGAA_2024_44_2_a6,
     author = {Pantarak, Thapakorn and Chaiya, Yanisa},
     title = {A note on intra regularity on semigroups of partial transformations with invariant set},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {333--341},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a6/}
}
TY  - JOUR
AU  - Pantarak, Thapakorn
AU  - Chaiya, Yanisa
TI  - A note on intra regularity on semigroups of partial transformations with invariant set
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2024
SP  - 333
EP  - 341
VL  - 44
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a6/
LA  - en
ID  - DMGAA_2024_44_2_a6
ER  - 
%0 Journal Article
%A Pantarak, Thapakorn
%A Chaiya, Yanisa
%T A note on intra regularity on semigroups of partial transformations with invariant set
%J Discussiones Mathematicae. General Algebra and Applications
%D 2024
%P 333-341
%V 44
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a6/
%G en
%F DMGAA_2024_44_2_a6
Pantarak, Thapakorn; Chaiya, Yanisa. A note on intra regularity on semigroups of partial transformations with invariant set. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 333-341. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a6/

[1] W. Choomanee, P. Honyam and J. Sanwong, Regularity in semigroups of transformations with invariant sets, Int. J. Pure Appl. Math. 87(1) (2013) 151–164. https://doi.org/10.12732/ijpam.v87i1.9

[2] A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups, Vol. I, Mathematical Surveys, 7 (American Mathematical Society, Providence, R.I., 1961). https://doi.org/10.1090/surv/007.1

[3] A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups, Vol. II, Mathematical Surveys, 7 (American Mathematical Society, Providence, R.I., 1967). https://doi.org/10.1090/surv/007.2

[4] C. Doss, Certain Equivalence Relations in Transformation Semigroups, Master's thesis, directed by D.D. Miller (University of Tennessee, 1955).

[5] 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

[6] J.M. Howie, Fundamentals of Semigroup Theory (London Mathematical Society Monographs, New Series, 12, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995).

[7] K.D. Jr. Magill, Subsemigroups of S(X), Math. Japonica 11 (1966) 109–115.