On geometrical hyperstructures of finite order

Authors

  • Achilles Dramalidis School of Sciences of Education, Democritus University of Thrace, 681 00 Alexandroupolis, Greece

Keywords:

Hypergroups, Hv-groups, Hv-rings

Abstract

It is known that a concrete representation of a finite k-dimensional Projective Geometry can be given by means of marks of a Galois Field GF [p^n], denoted by PG(k, p^n).
In this geometry, we define hyperoperations, which create hyperstructures of finite order and we present results, propositions and examples on this topic. Additionally, we connect these hyperstructures to Join Spaces.

References

Carmichael R.: Introduction to the theory of Groups of Finite Order, Dover Publications, Inc., New York.

Corsini P. : Prolegomena of hypergroup theory, Second edition, Aviani (1993).

Corsini P. – Leoreanu V. : Applications of Hyperstructures Theory, Kluwer Academic Publishers, Boston / Dordrecht / London.

Dramalidis, A., Dual Hv-rings, Rivista di Mathematica Pura ed Applicata, vol. 17, 55-62 (1996).

Marty F. : Sur une generalization de la notion de group, 8iem congres Math. Scandinaves, Stockholm (1934), 45-49.

Prenowitz W. – Jantosciak J.: Geometries and join spaces, Journal Mathematic, v. 257, 101-128 (1972).

Veblen O. – Bussey W.H.: Finite projective geometries, Trans. Amer. Math. Soc., v. 7, 241-259 (1906).

Vougiouklis T. : The fundamental relation in hyperrings. The general hyperfield, Proc. of the 4th AHA, Xanthi (1990), World Scientific, 1991, 203 – 211.

Vougiouklis T. : Hyperstructures and their representations, Monographs, Hadronic Press 1994, USA.

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Published

2011-12-18

Issue

Vol. 21 (2011)

Section

Volume 21-2011

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