IJPAM: Volume 118, No. 1 (2018)

Title

ON LEFT AND RIGHT BASES OF A $\Gamma$-SEMIGROUP

Authors

Thawhat Changphas$^2$, Pisit Kummoon$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Khon Kaen University
Khon Kaen, 40002, THAILAND
Centre of Excellence in Mathematics, CHE, Si Ayuttaya Rd.,
Bangkok 10400, THAILAND

Abstract

In the line of I. Frabrici [I. Fabrici, One-sided bases of semigroups, Matematický casopis, 22(4), 1972, 286-290], the notions of left and right bases of a $\Gamma$-semigroup are introduced, and some examples are also presented. The structure of a $\Gamma$-semigroup containing right bases will be studied. Indeed, using a characterization of right bases, we prove that the right bases of a $\Gamma$-semigroup have the same cardinality. Moreover, the compliment of the union of all right bases of a $\Gamma$-semigroup, if it is non-empty, is a left ideal of the $\Gamma$-semigroup. Finally, a characterization when the compliment of the union of all right bases of a $\Gamma$-semigroup is maximal will be given.

History

Received: 2017-10-30
Revised: 2018-02-08
Published: February 18, 2018

AMS Classification, Key Words

AMS Subject Classification: 20M20, 15A04
Key Words and Phrases: $\Gamma$-semigroup, left (right) $\Gamma$-ideal, left (right) base

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Bibliography

1
A. Iampan, Note on bi-ideals in $\Gamma$-semigroups, Int. J. Algebra Comput., 3 (2009), 181-188.

2
A. Iampan, On bi-ideals of semigroups, Lobachevskii J. Math., 29 (2008),68-72.

3
H. Hedayati, K. P. Saha, An introduction to $\Gamma$-semigroups, International Journal of Algebra, 15 (2011), no. $5$, 709-726.

4

How to Cite?

DOI: 10.12732/ijpam.v118i1.12 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: 2018
Volume: 118
Issue: 1
Pages: 125 - 135


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