Transformation semigroups associated to Γ-semigroups
Dariush Heidari ; Marzieh Amooshahi
Discussiones Mathematicae - General Algebra and Applications, Tome 33 (2013), p. 249-259 / Harvested from The Polish Digital Mathematics Library
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The concept of Γ-semigroups is a generalization of semigroups. In this paper, we associate two transformation semigroups to a Γ-semigroup and we call them the left and right transformation semigroups. We prove some relationships between the ideals of a Γ-semigroup and the ideals of its left and right transformation semigroups. Finally, we study some relationships between Green's equivalence relations of a Γ-semigroup and its left (right) transformation semigroup.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:270760 
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     author = {Dariush Heidari and Marzieh Amooshahi},
     title = {Transformation semigroups associated to $\Gamma$-semigroups},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {33},
     year = {2013},
     pages = {249-259},
     zbl = {1301.20066},
     language = {en},
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Dariush Heidari; Marzieh Amooshahi. Transformation semigroups associated to Γ-semigroups. Discussiones Mathematicae - General Algebra and Applications, Tome 33 (2013) pp. 249-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1204/

[000] [1] S.M. Anvariyeh, S. Mirvakili and B. Davvaz, On Γ-hyperideals in Γ-semihypergroups, Carpathian 26 (2010) 11-23. | Zbl 1197.20061

[001] [2] R. Chinram and P. Siammai, On Green's relations for Γ-semigroups and reductive Γ-semigroups, Int. J. Algebra 2 (2008) 187-195. | Zbl 1143.20044

[002] [3] A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups (American Mathematical Society, 1967). | Zbl 0178.01203

[003] [4] T.K. Dutta and N.C. Adhikari, On Noetherian Γ-semigroup, Kyungpook Math. J. 36 (1996) 89-95. | Zbl 0872.20055

[004] [5] T.K. Dutta and N.C. Adhikary, On Γ-semigroup with right and left unities, Soochow J. of Math 19(4) (1993) 461-474. | Zbl 0802.20053

[005] [6] D. Heidari, S.O. Dehkordi and B. Davvaz, Γ-Semihypergroups and their properties, UPB. Sci. Bull. Ser A 72(1) (2010) 197-210. | Zbl 1197.20062

[006] [7] D. Heidari and B. Davvaz, Γ-hypergroups and Γ-Semihypergroups associated to binary relations, Iran. J. Sci. Technol. Trans. A Sci. A2 (2011) 69-80.

[007] [8] J.A. Green, On the structure of semigroups, Annal of Mathematics 54 (1951) 163-172. doi: 10.2307/1969317. | Zbl 0043.25601

[008] [9] N.K. Saha, On Γ-semigroup II, Bull. Cal. Math. Soc. 79 (1987) 331-335.

[009] [10] M.K. Sen, On Γ-semigroups, in: Int. Conf. on Algebra and it's Appl, Decker Publication (Ed(s)), (New York, 1981).

[010] [11] M.K. Sen and N.K. Saha, On Γ-semigroup I, Bull. Cal. Math. Soc. 78 (1986) 180-186.

[011] [12] A. Seth, Γ-group congruences on regular Γ-semigroups, Int. J. Math. Math. Sci. (1992) 103-106. | Zbl 0746.20051

[012] [13] M. Siripitukdet and A. Iampan A, On the Ideal Extensions in Γ-semigroups, Kyungpook Math. J. 48 (2008) 585-591. doi: 10.5666/KMJ.2008.48.4.585.

[013] [14] M. Siripitukdet and A. Iampan, Least Regular Order with Respect to a Regular Congruence on Ordered Γ-Semigroups, Acta Mathematica Sinica, English Series 28(5) (2012) 975-982. doi: 10.1007/s10114-011-9702-x.