On Sperner \(\Gamma\)-(semi)hypergroups

Authors

  • M. Iranmanesh Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan
  • M. Jafarpour Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan
  • H. Aghabozorgi Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan

DOI:

https://doi.org/10.26713/cma.v8i1.501

Keywords:

Sperner \(\Gamma\)-(semi)hypergroup, complete \(\Gamma\)-(semi)hypergroup, complentable \(\Gamma\)-(semi)hypergroups

Abstract

In this paper first we use the notion of Sperner family and we introduce some classes of \(\Gamma\)-(semi)hypergroups that we call them weak Sperner \(\Gamma\)-(semi)hypergroups and Sperner \(\Gamma\)-(semi)hypergroups. Then we introduce the class of complete \(\Gamma\)-(semi)hypergroups as a generalization of the class of complete semihypergroups and we show that every complete \(\Gamma\)-(semi)hypergroups is a Sperner \(\Gamma\)-(semi)hypergroups. Finally the class of complementable \(\Gamma\)-(semi)hypergroups is investigated.

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References

S.M. Anvariyeh, S. Mirvakili and B. Davvaz, On (Gamma)-hyperideals in ¡-semihypergroups, Carpathian Journal of Mathematics 26 (1) (2010), 11 – 23.

S. Chattopadhyay, Right inverse (Gamma)-semigroup, Bull. Cal. Math. Soc. 93 (2001), 435 – 442.

S. Chattopadhyay, Right orthodox (Gamma)-semigroup, Southeast Asian Bull. Math. 29 (2005), 23 – 30.

R. Chinram and C. Jirojkul, On bi-(Gamma)-ideals in (Gamma)-semigroups, Songklanakarin J. Sci. Technol. 29 (2007), 231 – 234.

R. Chinram and P. Siammai, On Green's relations for (Gamma)-semigroups and reductive ¡-semigroups, Int. J. Algebra 2 (2008), 187 – 195.

P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers (2003).

D. Heidari, S.O. Dehkordi and B. Davvaz, (Gamma)-semihypergroups and their properties, University Politehnica of Bucharest Scientific Bulletin, Series A 72 (1) (2010), 195 – 208.

K. Hila, On regular, semiprime and quasi-reflexive (Gamma)-semigroup and minimal quasi-ideals, Lobachevski J. Math. 29 (2008), 141 – 152.

K. Hila, On some classes of le-(Gamma)-semigroups, Algebras Groups Geom. 24 (2007), 485 – 495.

M. Jafarpour, H. Aghabozorgi and V. Leoreanu-Fotea, On Sperner (semi)hypergroups, European Journal of Combinatorics 44 (Part B) (2015), 231 – 235.

M. Jafarpour, S.S. Mousavi and V. Leoreanu-Fotea, A class of semihypergroups connected to preordered weak ¡-semigroups, Computers & Mathematics with Applications 62 (I8) (2011), 2944 – 2949.

F. Marty, Sur une generalization de la notion de groupe, 8iem Congres Math. Scandinaves, Stockholm (1934), 45 – 49.

N.K. Saha, On (Gamma)-semigroup II, Bull. Cal. Math. Soc. 79 (1987), 331 – 335.

M.K. Sen and S. Chattopadhyay, Semidirect product of a monoid and a ¡-semigroup, East-West J. Math. 6 (2004), 131 – 138.

M.K. Sen and A. Seth, On po-(Gamma)-semigroups, Bull. Calcutta Math. Soc. 85 (1993), 445 – 450.

M.K. Sen and N.K. Saha, Orthodox (Gamma)-semigroups, Internat. J. Math. Math. Sci. 13 (1990), 527 – 534.

M.K. Sen and N.K. Saha, On (Gamma)-semigroup I, Bull. Cal. Math. Soc. 78 (1986), 180 – 186.

A. Seth, (Gamma)-group congruences on regular (Gamma)-semigroups, Internat. J. Math. Math. Sci. 15 (1992), 103 – 106.

Z.X. Zhong and M.K. Sen, On several classes of orthodox (Gamma)-semigroups, J. Pure Math. 14 (1997), 18 – 25.

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Published

30-06-2017
CITATION

How to Cite

Iranmanesh, M., Jafarpour, M., & Aghabozorgi, H. (2017). On Sperner \(\Gamma\)-(semi)hypergroups. Communications in Mathematics and Applications, 8(1), 61–68. https://doi.org/10.26713/cma.v8i1.501

Issue

Vol. 8 No. 1 (2017)

Section

Research Article

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