Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Analele Universitatii "Ovidius" Constanta - Seria Matematica

The Journal of "Ovidius" University of Constanta

Editor-in-Chief: Flaut, Cristina

1 Issue per year

IMPACT FACTOR 2016: 0.422

CiteScore 2016: 0.56

SCImago Journal Rank (SJR) 2016: 0.346
Source Normalized Impact per Paper (SNIP) 2016: 0.966

Mathematical Citation Quotient (MCQ) 2016: 0.10

Open Access
See all formats and pricing
More options …

Composition hyperrings

Irina Cristea
  • Corresponding author
  • Centre for Systems and Information Technologies, University of Nova Gorica SI-5000, Vipavska 13, Nova Gorica, Slovenia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Sanja Jančić-Rašović
  • Department of Mathematics, Faculty of Natural Science and Mathematics, University of Montenegro, Dzordza Vasingtona bb, 81000 Podgorica, Montenegro
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-09-19 | DOI: https://doi.org/10.2478/auom-2013-0024


In this paper we introduce the notion of composition hyperring. We show that the composition structure of a composition hyperring is determined by a class of its strong multiendomorphisms. Finally, the three isomorphism theorems of ring theory are derived in the context of com- position hyperrings.

Keywords: Hyperring; Hyperideal; Multiendomorphism; Composition hyperoperation

  • [1] I. Adler, Composition rings, Duke Math. J., 29 (1962), 607-623.Google Scholar

  • [2] H. Babaei, M. Jafarpour, S.Sh. Mousavi, R-parts in hyperrings, Iran. J. Math. Sci. Inform., 7(2012), no.1, 59-71.Google Scholar

  • [3] J. Chvalina, S. Hoskova-Mayerova, A.D. Nezhad, General actions of hy­perstructures and some applications, An. Stiint. Univ. Ovidius Constanta Ser. Mat., 21(2013), no.1, 59-82.Google Scholar

  • [4] A. Connes, C. Consani, The hyperring of adele classes, J. Number Theory, 131(2011), no.2, 159-194.Google Scholar

  • [5] B. Davvaz, A. Salasi, A realization of hyperrings, Comm. Algebra, 34(2006), 4389-4400.Google Scholar

  • [6] B. Davvaz, V. Leoreanu-Fotea, Hyperring theory and applications, Inter­national Accademic Press, Palm Harbor, U.S.A., 2007.Google Scholar

  • [7] S. Jančić-Rašović, About the hyperring of polynomials, Ital. J. Pure Appl. Math., 21(2007), 223-234.Google Scholar

  • [8] S. Jancic-Rasovic, On a class of Chinese Hyperrings, Ital. J. Pure Appl. Math., 28(2011), 245-256.Google Scholar

  • [9] M. Krasner, Approximations des corps values complets de characteris- tique p = 0 par ceux de characteristique 0, Colloque d’Algebre Superieure, CBRM, Bruxelles, 1956.Google Scholar

  • [10] M. Krasner, A class of hyperrings and hyperfields, Int. J. Math. Math. Sci., 6(1983), no.2, 307-312.CrossrefGoogle Scholar

  • [11] Ch.G. Massouros, On the theory of hyperrings and hyperfields, Algebra i Logika, 24(1985), 728-742.Google Scholar

  • [12] G. G. Massouros, Fortified Join Hypergroups and Join Hyperrings, An. Stiint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 41(1995), 37-44.Google Scholar

  • [13] S. Mirvakili, B. Davvaz, Relations on Krasner (m, n)-hyperrings, Euro­pean J. Combin., 31(2010), 790-802.Google Scholar

  • [14] J. Mittas, Hyperanneaux canoniques, Math. Balkanica, 2(1972), 165-179.Google Scholar

  • [15] J. Mittas, Sur les hyperanneaux et les hypercorps, Math. Balkanica, 3(1973), 368-382.Google Scholar

  • [16] A. Nakassis, Recent results in hyperring and hyperfield theory, Int. J. Math. Math. Sci., 11(1988), 209-220.CrossrefGoogle Scholar

  • [17] W. Phanthawimol, Y. Punkla, K. Kwakpatoon, Y. Kemprasit, On homo- morphisms of Krasner hyperrings, An. Stiint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 57(2011), 239-246.Google Scholar

  • [18] S. Spartalis, A class of hyperrings, Riv. Mat. Pura Appl., 4(1989), 55-64.Google Scholar

  • [19] S. Spartalis, (H, R)-hyperrings, Algebraic hyperstructures and applica­tions (Xanthi, 1990), 187195, World Sci. Publ., Teaneck, NJ, 1991.Google Scholar

  • [20] D. Stratigopoulos, Hyperanneaux non commutatifs: Le radical d’un hy- peranneau, somme sous-directe des hyperanneaux artiniens et theorie des elements idempotents, C.R. Acad. Sci. Paris, 269(1969), 627-629.Google Scholar

  • [21] O. Viro, On basic concepts of tropical geometry, Tr. Mat. Inst. Steklova, 273(2011), Sovremennye Problemy Matematiki, 271-303.Google Scholar

  • [22] T. Vougiouklis, The fundamental relation in hyperrings. The general hy­perfields, Algebraic hyperstructures and applications (Xanthi, 1990), 203­211, World Sci. Publ., Teaneck, NJ, 1991.Google Scholar

About the article

Published Online: 2013-09-19

Published in Print: 2013-06-01

Citation Information: Analele Universitatii "Ovidius" Constanta - Seria Matematica, Volume 21, Issue 2, Pages 81–94, ISSN (Online) 1844-0835, DOI: https://doi.org/10.2478/auom-2013-0024.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

M. Al Tahan and B. Davvaz
Journal of Number Theory, 2017

Comments (0)

Please log in or register to comment.
Log in