On P-H_v-Structures in a Two-Dimensional Real Vector Space

Authors

  • Ioanna Iliou Democritus University of Thrace, School of Education
  • Achilles Dramalidis Democritus University of Thrace, School of Education

DOI:

https://doi.org/10.23755/rm.v33i0.381

Keywords:

Hyperstructures, Hv-structures, hopes, P-hyperstructures.

Abstract

In this paper we study P-Hv-structures in connection with Hv-structures, arising from a specific P-hope in a two-dimensional real vector space. The visualization of these P-Hv-structures is our priority, since visual thinking could be an alternative and powerful resource for people doing mathematics. Using position vectors into the plane, abstract algebraic properties of these P-Hv-structures are gradually transformed into geometrical shapes, which operate, not only as a translation of the algebraic concept, but also, as a teaching process.  

Author Biographies

  • Ioanna Iliou, Democritus University of Thrace, School of Education

    Department of Primary Level Education

    Postgraduate student

  • Achilles Dramalidis, Democritus University of Thrace, School of Education

    Department of Education Sciences in Early Childhood

    Professor

References

Corsini P., Prolegomena of Hypergroup Theory, Aviani Editore, 1993.

Corsini P., Leoreanu V., Application of Hyperstructure Theory, Klower Ac. Publ., 2003.

Davvaz B., Leoreanu-Fotea V., Hyperring Theory and Applications, Int.Acad. Press, USA, 2007.

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

Dramalidis A., Some geometrical P-HV-structures, New Frontiers in Hyperstructures, Hadronic Press, USA, (1996), 93-102.

Dramalidis A., Geometrical Hv-structures, Proceedings: Structure Elements of Hyperstructures, Spanidis, 2005.

Dramalidis A., Dual Hv-rings, Rivista di Matematica Pura ed Applicata, Italy, v. 17, (1996), 55-62.

Dramalidis A., Mahjoob R., Vougiouklis T., P-hopes on non-square matrices for Lie-Santilli Admissibility, Clifford Analysis, Clifford Algebras and their Applications, CSP-Cambridge, UK; I&S-Florida, USA, Vol.4, No.4, (2015), 361-372.

Dramalidis A., Vougiouklis T., On a class of geometric fuzzy Hv-structures, 8th AHA Congress, Samothraki, Greece, 2002.

Dramalidis A., Vougiouklis T., Fuzzy Hv-substructures in a two dimensional Euclidean vector space, Iranian J. Fuzzy Systems, 6(4), (2009), 1-9.

Dramalidis A., Visualization of Algebraic Properties of Special Hv-structures, Ratio Mathematica, Italy, v. 24, (2013), 41-52.

Koskas M., Groupoides demi-hypergroupes et hypergroupes, J. Math. Pures Appl., 49 (9), (1970), 155-192.

Vougiouklis T., The fundamental relation in hyperrings. The general hyperfield, 4th AHA Congress, World Scientific, (1991), 203-211.

Vougiouklis T., Hyperstructures and their Representations, Monographs Math., Hadronic Press, 1994.

Vougiouklis T., On Hv-rings and Hv-representations, Discrete Math. 208/209, (1999), 615-620.

Vougiouklis T., Lie-Santilli Admissibility using P-hyperoperations on matrices, Hadronic J. 7, (2014), 1-14.

Vougiouklis T., Some remarks on hyperstructures, Contemporary Mathematics, Amer. Math. Society 184, (1995), 427–431.

Vougiouklis T., A new class of hyperstructures, J.C.I. & S.S. 20, (1995), 229–239.

Vougiouklis T., Representations of hypergroups by generalized permutations, Algebra Universalis, 29, (1992), 172-183.

Vougiouklis T., Some remarks on hyperstructures, Contemporary Math., Amer. Math. Society, 184, (1995), 427-431.

Vougiouklis T., Generalization of P-hypergroups, Rend. Circolo Mat. Palermo Ser.II (1987), 114–121.

Vougiouklis T., Cyclicity in a special class of hypergroups, Acta Un. Car. Math. Et Ph. 22, (1981), 3–6.

Vougiouklis T., Generalization of P-hypergroups, Rend. Circolo Mat. Palermo Ser.II (1987), 114–121.

Vougiouklis T., Dramalidis A., Hv-modulus with external P-hyperoperations, Proc. of the 5th AHA, Iasi, Romania, (1993), 191-197.

Downloads

Published

2017-12-28

Issue

Vol. 33 (2017)

Section

Volume 33-2017

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.