Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 1

Composition in EL–hyperstructures

Pages
45–58
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In our paper we link this concept to the concept of a composition hyperring, a recent hyperstructure generalization of the classical notion of a composition ring.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The link between ordered sets and hyperstructures is one of the classical areas of research in the hyperstructure theory.
📊
Key Findings & Data:In this paper we focus on EL–hyperstructures, i.e. a class of hyperstructures constructed from quasi-ordered semigroups.
💡
Conclusion & Impact:In our paper we link this concept to the concept of a composition hyperring, a recent hyperstructure generalization of the classical notion of a composition ring.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The link between ordered sets and hyperstructures is one of the classical areas of research in the hyperstructure theory. In this paper we focus on EL–hyperstructures, i.e. a class of hyperstructures constructed from quasi-ordered semigroups. In our paper we link this concept to the concept of a composition hyperring, a recent hyperstructure generalization of the classical notion of a composition ring.

🔖

Cite This Article

NOVAK, M., CRİSTEA, I. (2022). Composition in EL–hyperstructures. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 1, 45–58. https://ajindex.com/articles/530087

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (20)

  1. I. Adler, Composition rings, Duke Math. J. 29, 607-623, 1962
  2. S. M. Anvariyeh and B. Davvaz, Strongly transitive geometric spaces associated to hypermodules, J. Algebra 332, 1340-1359, 2009
  3. J. Chvalina, Commutative hypergroups in the sense of Marty and ordered sets, General Algebra and Ordered Sets, Proc. Int. Conf. Olomouc, 19-30, 1994
  4. J. Chvalina, Functional Graphs, Quasi-ordered Sets and Commutative Hypergroups (in Czech), Masaryk University, Brno, 1995
  5. J. Chvalina and L. Chvalinová, Transposition hypergroups formed by transformation operators on rings of differentiable functions, Ital. J. Pure Appl. Math. 15, 93-106, 2004
  6. J. Chvalina, Š. Hošková–Mayerová and A.D. Nezhad, General actions of hyperstruc- tures and some applications, An. Şt. Univ. Ovidius Constanta, 21 (1), 59-82, 2013
  7. A. Connes and C. Consani, The hyperring of adéle classes, J. Number Theory 131 (2), 159-194, 2011
  8. P. Corsini, Hyperstructures associated with ordered sets, Bull. Greek Math. Soc. 48, 7-18, 2003
  9. P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Academic Publishers, Dodrecht, 2003
  10. I. Cristea and S. Jančić-Rašović, Composition hyperrings, An. Şt. Univ. Ovidius Con- stanţa 21 (2), 81-94, 2013
  11. B. Davvaz and V. Leoreanu Fotea, Applications of Hyperring Theory, International Academic Press, Palm Harbor, 2007
  12. B. Davvaz, N. Rakhsh-Khorshid and K.P. Shum, Construction of composition (m, n, k)–hyperrings, An. Şt. Univ. Ovidius Constanţa 24 (1), 177-188, 2016
  13. B. Davvaz and A. Salasi, A realization of hyperrings, Comm. Algebra 34, 4389-4400, 2006
  14. A. Deghan Nezhad and B. Davvaz, An Introduction to the Theory of Hv–Semilattices, Bull. Malays. Math. Sci. Soc. 32 (3), 375-390, 2009
  15. S.H. Ghazavi and S.M. Anvariyeh, EL–hyperstructures associated to n-ary relations, Soft Comput. 21 (19), 5841-5850, 2017
  16. D. Heidari and B. Davvaz, On ordered hyperstructures, U.P.B. Sci. Bull. Series A, 73 (2), 2011
  17. K. Iwasava, On linearly ordered groups, J. Math. Soc. 1 (1), 1-9, 1948
  18. S. Jančić-Rašović, About the hyperring of polynomials, Ital. J. Pure Appl. Math. 28, 223-234, 2007
  19. M. Krasner, A class of hyperrings and hyperfields, Int. J. Math. Sci. 6 (2), 307-312, 1983
  20. M. Krasner, Approximation des corps values complets de characteristique p 6 = 0 par ceux de characteristique 0, Colloque d’Algebre Superieure, CBRM, Bruxelles, 1957. [21] Š. Křehlík and M. Novák, From lattices to Hv