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2013 | 33 | 2 | 249-259
Tytuł artykułu

Transformation semigroups associated to Γ-semigroups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
33
Numer
2
Strony
249-259
Opis fizyczny
Daty
wydano
2013
otrzymano
2013-08-17
poprawiono
2013-09-10
Twórcy
  • Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran
  • Department of Mathematics, Najafabad Branch, Islamic Azad University Najafabad, Isfahan, Iran
Bibliografia
  • [1] S.M. Anvariyeh, S. Mirvakili and B. Davvaz, On Γ-hyperideals in Γ-semihypergroups, Carpathian 26 (2010) 11-23.
  • [2] R. Chinram and P. Siammai, On Green's relations for Γ-semigroups and reductive Γ-semigroups, Int. J. Algebra 2 (2008) 187-195.
  • [3] A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups (American Mathematical Society, 1967).
  • [4] T.K. Dutta and N.C. Adhikari, On Noetherian Γ-semigroup, Kyungpook Math. J. 36 (1996) 89-95.
  • [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.
  • [6] D. Heidari, S.O. Dehkordi and B. Davvaz, Γ-Semihypergroups and their properties, UPB. Sci. Bull. Ser A 72(1) (2010) 197-210.
  • [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.
  • [8] J.A. Green, On the structure of semigroups, Annal of Mathematics 54 (1951) 163-172. doi: 10.2307/1969317.
  • [9] N.K. Saha, On Γ-semigroup II, Bull. Cal. Math. Soc. 79 (1987) 331-335.
  • [10] M.K. Sen, On Γ-semigroups, in: Int. Conf. on Algebra and it's Appl, Decker Publication (Ed(s)), (New York, 1981).
  • [11] M.K. Sen and N.K. Saha, On Γ-semigroup I, Bull. Cal. Math. Soc. 78 (1986) 180-186.
  • [12] A. Seth, Γ-group congruences on regular Γ-semigroups, Int. J. Math. Math. Sci. (1992) 103-106.
  • [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.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1204
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