Vougiouklis Contributions in the Field of Algebraic Hyperstructures

Bijan Davvaz


Thomas Vougiouklis was born in 1948,  Greece. He  has many contributions to algebraic hyperstructures. $H_v$-structures are  some of his main contributions. In this article, we study some of Vougiouklis ideas in the field of algebraic hyperstructures as follows: (1) Semi-direct hyperproduct of two hypergroups; (2) Representation of hypergroups; (3) Fundamental relation in hyperrings; (4) Commutative rings obtained from hyperrings; (5) $H_v$-structures; (6) The uniting elements method; (7) The e-hyperstructures;
(8) Helix-hyperoperations.


hyperoperation, hypergroup, hyperring, $H_v$-group, $H_v$-ring, fundamental relation

Full Text:



P. Corsini and T. Vougiouklis, From groupoids to groups through hyper-groups, Rend. Mat. Appl. (7), 9 (1989), 173-181.

B. Davvaz, A brief survey of applications of generalized algebraic struc-tures and Santilli-Vougiouklis hyperstructures, Third International Confer-ence on Lie-Admissible Treatment of Irreversible Processes (ICLATIP-3), Kathmandu University, Nepal, April (2011), 91-110.

B. Davvaz, S. Vougiouklis and T. Vougiouklis, On the multiplicative Hv-rings derived from helix hyperoperations, Utilitas Mathematica, 84 (2011), 53-63.

B. Davvaz and T. Vougiouklis, Commutative rings obtained from hyperrings (Hv-rings) with -relations, Communications in Algebra, 35 (2007), 3307-3320.

B. Davvaz, R. M. Santilli and T. Vougiouklis, Studies of multivalued hy-perstructures for the characterization of matter-antimatter systems and their extension, Algebras Groups and Geometries, 28 (2011), 105-116.

B. Davvaz, R. M. Santilli and T. Vougiouklis, Multi-Valued Hypermathe-matics for Characterization of Matter and Antimatter Systems, Journal of Computational Methods in Sciences and Engineering (JCMSE), 13 (2013), 37-50.

B. Davvaz, R. M. Santilli and T. Vougiouklis, Mathematical prediction of Ying’s twin universes, American Journal of Modern Physics, 4(3) (2015), 5-9.

B. Davvaz, R. M. Santilli and T. Vougiouklis, Algebra, Hyperalgebra and Lie-Santilli Theory, Journal of Generalized Lie Theory and Applications, 9(2) (2015), 231.

D. Freni, Une note sur le cour d’un hypergroupe et sur la clotureˆ transitive de . (French) [A note on the core of a hypergroup and the transitive closure of ], Riv. Mat. Pura Appl., 8 (1991), 153-156.

M. Koskas, Groupoides, demi-hypergroupes et hypergroupes, J. Math. Pures Appl, 49 (1970), 155-192.

R.M. Santilli and T. Vougiouklis, Isotopies, genotopies, hyperstructures and their applications, in New frontiers in hyperstructures (Molise, 1995), pp. 1-48, Ser. New Front. Adv. Math. Ist. Ric. Base, Hadronic Press, Palm Harbor, FL, 1996.

S. Spartalis and T. Vougiouklis, The fundamental relations of Hv-rings, Riv. Mat. Pura Appl., 14 (1994) 7-20.

T. Vougiouklis, Groups in hypergroups, Annals of Discrete Mathematics, 37 (1988), 459-468.

T. Vougiouklis, Representation of hypergroups. Hypergroup algebra

T. Vougiouklis, On some representations of hypergroups, Annales Sci. Univ. “Blaise Pascal”, Clermont II, Ser. Math., 26 (1991), 21-29.

T. Vougiouklis, The fundamental relation in hyperrings. The general hyper-field, Algebraic hyperstructures and applications (Xanthi, 1990), 203-211, World Sci. Publishing, Teaneck, NJ, 1991.

T. Vougiouklis, Hypergroups, hyperrings. Fundamental relations and rep-resentations, Quaderni del Seminario di Geometria Combinatoria (1989), 1-20.

T. Vougiouklis, Hv-vector spaces, Algebraic hyperstructures and applica-tions (Iasi, 1993), 181-190, Hadronic Press, Palm Harbor, FL, 1994.

T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Inc., Palm Harbor, USA, 1994.

T. Vougiouklis, A new class of hyperstructures, J. Combin. Inform. System Sci., 20 (1995), 229-235.

T. Vougiouklis, Hv-groups defined on the same set, Discrete Math., 155 (1996), 259-265.

T. Vougiouklis, S. Spartalis and M. Kessoglides, Weak hyperstructures on small sets, Ratio Math., 12 (1997), 90-96.

T. Vougiouklis and S. Vougiouklis, The helix hyperoperations, Italian J. Pure Appl. Math., 18 (2005), 197-206.

S. Vougiouklis, Hv-vector spaces from helix hyperoperations,

DOI: http://dx.doi.org/10.23755/rm.v33i0.380


  • There are currently no refbacks.

Copyright (c) 2017 Bijan Davvaz

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.