IJPAM: Volume 108, No. 2 (2016)

GREEN'S RELATIONS ON SEMIGROUPS OF
REGRESSIVE TRANSFORMATIONS
WITH RESTRICTED RANGE

Kritsada Sangkhanan
Department of Mathematics
Faculty of Science
Chiang Mai University
Chiang Mai, THAILAND

Abstract. Let $X'$ be a subposet of a poset $X$. Define $\pre$ be the semigroup under composition of all regressive transformations from a subset of $X$ into $X'$. Moreover,

\begin{displaymath}
\tre=\{\alpha\in\pre : \dom\alpha=X\}.
\end{displaymath}

In 2012, C. Namnak and E. Laysirikul [3] investigated the Green's relations on $T_{RE}(X)=T_{RE}(X,X)$. Now, we aim to extend the result of them by study the Green's relations on the semigroups $\tre$ and $\pre$.

Received: Marhc 26, 2016

Revised: Marhc 26, 2016

Published: October 1, 2016

AMS Subject Classification: 20M20

Key Words and Phrases: poset, regressive transformations, restricted range, Green's relations
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Bibliography

1
P. Jitjankarn and P. Udomkavanich, Regularity of some regressive transformation semigroups, East-West Journal of Mathematics, Special Vol. (2004), 111-118.

2
Y. Kemprasit, Quasi-regular regressive transformation semigroups, Southeast Asian Bulletin of Mathematics, 26 (2003), 955-959.

3
C. Namnak and E. Laysirikul, Regularity and Green's relations for the full regressive transformation semigroups, International Journal of Algebra, 6, 17-20 (2012), 919-925.

4
P. Udomkavanich and P. Jitjankarn, Isomorphism theorems of regressive partial transformation semigroups, Italian Journal of Pure and Applied Mathematics, 18 (2005), 207-212.

5
P. Udomkavanich and P. Jitjankarn, Some isomorphism theorems on regressive transformation semigroups, Southeast Asian Bulletin of Mathematics, 29, 3 (2005), 581.

6
P. Udomkavanich and P. Jitjankarn, A classification of regressive transformation semigroups on chains, Semigroup Forum, 85, 3 (2012), 559-570. doi:10.1007/s00233-012-9438-7

7
A. Umar, Semigroups of order-decreasing transformations: The isomorphism theorem, Semigroup Forum, 53, 1 (1996), 220-224. doi:10.1007/BF02574137

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DOI: 10.12732/ijpam.v108i2.19 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 2
Pages: 467 - 476


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