SavedAdd your journal

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

Composition in $EL$-hyperstructures

Michal Novak
Irina Cristea
Pages
45–58
Publication Date
2019-02-01
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 \emph{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 \emph{composition hyperring}, a recent hyperstructure generalization of the classical notion of a composition ring.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Composition ring · composition hyperring · hyperstructure theory

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 \emph{composition hyperring}, a recent hyperstructure generalization of the classical notion of a composition ring.

🔖

Cite This Article

Novak, M., Cristea, I. (2019). Composition in $EL$-hyperstructures. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 1, 45–58. https://ajindex.com/articles/669393

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  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. 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. J. Chvalina, Š. Hošková-Mayerová and A.D. Nezhad, General actions of hyperstructures and some applications, An. St. Univ. Ovidius Constanta, 21 (1), 59-82, 2013.
  5. A. Connes and C. Consani, The hyperring of adéle classes, J. Number Theory 131 (2), 159-194, 2011.
  6. P. Corsini, Hyperstructures associated with ordered sets, Bull. Greek Math. Soc. 48, 7-18, 2003.
  7. P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Academic Publishers, Dodrecht, 2003. I. Cristea and S. Jancic-Rašovic, Composition hyperrings, An. St. Univ. Ovidius Constanta 21 (2), 81-94, 2013.
  8. B. Davvaz and V. Leoreanu Fotea, Applications of Hyperring Theory, International Academic Press, Palm Harbor, 2007.
  9. B. Davvaz, N. Rakhsh-Khorshid and K.P. Shum, Construction of composition $(m,n,k)$-hyperrings, An. St. Univ. Ovidius Constanta 24 (1), 177-188, 2016.
  10. B. Davvaz and A. Salasi, A realization of hyperrings, Comm. Algebra 34, 4389-4400, 2006.
  11. A. Deghan Nezhad and B. Davvaz, An Introduction to the Theory of $H_v$-Semilattices, Bull. Malays. Math. Sci. Soc. 32 (3), 375-390, 2009. S.H. Ghazavi and S.M. Anvariyeh, $EL$-hyperstructures associated to $n$-ary relations, Soft Comput. 21 (19), 5841-5850, 2017.
  12. D. Heidari and B. Davvaz, On ordered hyperstructures, U.P.B. Sci. Bull. Series A, 73 (2), 2011.
  13. K. Iwasava, On linearly ordered groups, J. Math. Soc. 1 (1), 1-9, 1948. S. Jancic-Rašovic, About the hyperring of polynomials, Ital. J. Pure Appl. Math. 28, 223-234, 2007.
  14. M. Krasner, A class of hyperrings and hyperfields, Int. J. Math. Sci. 6 (2), 307-312, 1983.
  15. M. Krasner, Approximation des corps values complets de characteristique $p\not=0$ par ceux de characteristique 0, Colloque d’Algebre Superieure, CBRM, Bruxelles, 1957. Š. Krehlík and M. Novák, From lattices to $H_v$-matrices, An. St. Univ. Ovidius Constanta 24 (3), 209-222, 2016.
  16. Ch.G. Massouros, On th