On the Hypergroups Associated with $n$-ary Relations

Authors

  • S. Govindarajan Department of Mathematics, A.V.C. College (Autonomous), Mannampadal 609305, Tami Nadu
  • G. Ramesh P.G. and Research Department of Mathematics, Ramnujan Research Centre, Govt. Arts College (Autonomous), Kumbakonam 612001, Tamil Nadu

DOI:

https://doi.org/10.26713/jims.v6i2.244

Keywords:

$n$-ary relations, Hypergroups, Joinspces

Abstract

The paper deals with hypergroupoids associated with $n$-ary $3n\ge 35$ relations. We give necessary and sufficient condition for an $n$-ary relation such that the hypergroupoid associated with it is a hypergroup or a joinspace. First we analyze for sufficient condition using ternary relation such that the hypergroupoid associated with it is a hypergroup or a joinspace and then we generalize it for an $n$-ary relation.

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References

P. Corsini, Prolegomena of Hypergroup theory, Aviani editore, 1993.

P. Corsini, Hypergraphs and hypergroups, Algebra universalis, 35(1996), 548−555.

P. Corsini, On the hyper groups associated with binary relations, Multi. Val. Logic 5(2000), 407-407.

P. Corsini, Binary relations and hypergroupoids, Ital. J. Pure Appl. Math. 7(2000), 11−18.

P. Corsini, Binary relations, interval structures and join spaces, J. Appl.Math. Comput. 10(2002), 209−216.

P. Corsini and V. Leoreanu, Applications of hyperstructure Theory, in: Advances in Mathematics, Kluwer Academic Publishers, 2003.

P. Corsini and V. Leoreanu, Hypergroups and binary relations, Algebra universalis, 43(2000), 321-330.

P. Corsini and B. Davvaz, New connections among multivalued functions, hyper structures and fuzzy sets, JJMS 3(3) (2010), 133−150.

I. Cristea and M. Stefanescu, Binary relations and reduced hypergroups, Discrete Math. 308(2008), 3537−3544.

I. Cristea, Several aspects on the hypergroups associated with $n$-ary relation, Ovidius Constsnta Ser. Mat. 7(3) (2009), 90−110.

I. Cristea and M. Stefanescu, Hypergroups and $n$-ary relations, European Journal of Combin. 31 (2010), 780−789.

B. Davvaz and T. Vougiouklios, $N$-ary hypergroups, Iranian Journal of Scinence and Techonology, Transaction 30 (A2) (2006).

M. De Salvo and G. Lo Faro, Hyper groups and binary Relations, Multi. Val. logic 8 (5-6) (2002), 645-6574.

M. De Salvo and G. Lo Faro, A new class of hypergroupoids associated with binary relations, J. Multi. Val. Logic Soft Comput. 9 (4) (2003), 361−375.

A. Klopotowski, M. G. Nadkarni and K.P.S. Bhaskara Rao, Geometry of good sets in $n$-fold Cartesian produc, Proceedings of the Indian Academy of Sciences 114 (2), (May 2004), 181−197.

F. Marty, Sur une generalization de la notion de group, 8th Congress Math Scandenaves, Stockholm (1934), 45−49.

V. Leoreanu-Fotea and B. Davvaz, $n$-hypergroups and binary Relations, European. J. of Combin. 29(5) (2008), 1207−1218.

J. Nieminen, Join Space graphs, J. Goem, 33(1988), 99−103.

V. Novak, On representation of ternary structures, Math. Slovaca, 45(5) (1995), 469−480.

V. Novak and M. Novotony, Psedodimension of relational structures, Czechoslovak. Math. J. 49(124) (1999), 547−560.

I.G. Rosenberg, Hypergroups and join spaces determined by relations, Ital. J. Pure Appl. Math. 4 (1998) (2000), 93−101.

S. M. Anvariyeh and S. Momeni, $n$-ary hypergroups associated with $n$-ary relations, Bull. Korean Math. Soc. 50 (2) (2013), 507−524.

S. Spartalis, Hypergroupoids obtained from groupoids with binary relations, Ital. J. Pure Appl. Math. 16(24), 201−210.

S. Spartalis, The Hyperoperation Relation and the Corsini's partial ornot partial Hyper-groupoids: a classification, Ital. J. Pure Appl. Math. 24(2008), 97−112.

S. Spartalis and C. Mamaloukas, On hyperstuctures associated with binary relations, Comput. Math. Appl. 51(1) (2006), 41−50.

M. Stefanescu, Some interpretations of hypergroups, Bull.Math. Soc. Sc.Math. Roumanie. Tome. 48(96), 1 (2006), 99−104.

T. Vougioklis, Hyperstructures and their Representations,Hadronic Press, U.S.A., 1994.

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Published

2014-12-14
CITATION

How to Cite

Govindarajan, S., & Ramesh, G. (2014). On the Hypergroups Associated with $n$-ary Relations. Journal of Informatics and Mathematical Sciences, 6(2), 61–76. https://doi.org/10.26713/jims.v6i2.244

Issue

Vol. 6 No. 2 (2014)

Section

Research Articles

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