DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

T. Pantarak

Thapakorn Pantarak

Department of Mathematics and Statistics
Faculty of Science and Technology
Thammasat University, Pathum Thani, 12120, Thailand

email: thapakorn.pan@dome.tu.ac.th

Y. Chaiya

Yanisa Chaiya

Department of Mathematics and Statistics
Faculty of Science and Technology
Thammasat University
Pathum Thani, 12120, Thailand

email: yanisa@mathstat.sci.tu.ac.th

0000-0002-7119-2658

Title:

A note on intra regularity on semigroups of partial transformations with invariant set

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications 44(2) (2024) 333-341

Received: 2023-02-12 , Revised: 2023-05-15 , Accepted: 2023-05-16 , Available online: 2024-05-13 , https://doi.org/10.7151/dmgaa.1455

Abstract:

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 $$ \overline{PT}(X,Y) = \{\alpha \in P(X) : (\mathrm{dom\thinspace} \alpha \cap Y)\alpha \subseteq Y\}. $$ Then $\overline{PT}(X,Y)$ is a semigroup consisting of all mapping in $ P(X) $ that leave $ Y \subseteq X $ invariant. In this paper, we present criteria for checking the intra-regularity of elements in $\overline{PT}(X,Y)$ and apply these results to quantify intra-regular elements in $\overline{PT}(X,Y)$, when $X$ is finite.

Keywords:

partial transformation semigroup, intra regularity, invariant set

References:

  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.
Close