Abstract
This paper concerns a new relationship between hyperrings and rings. It is a continuation of ideas presented by Babaeia, Jafarpour, and Mousavi. We apply generalization of a complete part in a hyperring. We study the notion of strongly \(\mathcal {U}\)-regular relations on hyperrings and investigate some of their properties. In particular, we investigate the properties of rings derived from strongly \(\mathcal {U}\)-regular relations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anvariyeh, S.M., Davvaz, B.: Strongly transitive geometric spaces associated to hypermodules. J. Algebra 322, 1340–1359 (2009)
Babaeia, H., Jafarpourb, M., Mousavi, S.S.: \(\Re \)-parts in hyperrings. Iran. J. Math. Sci. Inf. 7(1), 59–71 (2012)
Corsini, P.: Prolegomena of Hypergroup Theory. Aviani Editore (1993)
Corsini, P., Leoreanu, V.: Applications of Hyperstructure Theory. Advances in Mathematics. Kluwer Academic Publishers, Amsterdam (2003)
Corsini, P., Leoreanu, V.: About the heart of a hypergroup. Acta Univ. Carol. 37, 17–28 (1996)
Davvaz, B., Salasi, A.: A realization of hyperrings. Commun. Algebra 34(12), 4389–4400 (2006)
Davvaz, B.: Applications of the \(\gamma ^*-\) relation to polygroups. Commun. Algebra 35, 2698–2706 (2007)
Davvaz, B.: Isomorphism theorems of hyperrings. Indian J. Pure Appl. Math. 35(3), 321–331 (2004)
Davvaz, B., Karimian, M.: On the \(\gamma ^*-\) complete hypergroups. Eur. J. Comb. 28, 86–93 (2007)
Davvaz, B., Leoreanu-Fotea, V.: Hyperring Theory and Applications. International Academic Press, New York (2007)
Davvaz, B., Vougiouklis, T.: Commutative rings obtained from hyperrings (\(H_v\)-rings) with \(\alpha ^*\)- relations. Commun. Algebra 35(11), 3307–3320 (2007)
Freni, D.: A new characterization of the derived hypergroup via strongly regular equivalences. Commun. Algebra 30(8), 3977–3989 (2002)
Freni, D.: Strongly transitive geometric spaces: applications to hypergroups and semigroups theory. Commun. Algebra 32(8), 969–988 (2004)
Koskas, M.: Groupoides, demi-hypergroupes et hypergroupes. J. Math. Pure Appl. 49, 155–192 (1970)
Krasner, M.: A class of hyperrings and hyperfields. Int. J. Math. Math. Sci. 6(2), 307–312 (1983)
Marty, F.: Sur une generalization de la notion de groupe. Congres Math, vol. 8, pp. 45–49. Stockholm, Scandinaves (1934)
Mirvakili, S., Anvariyeh, S.M., Davvaz, B.: Transitivity of \(\Gamma \)-relation on hyperfields. Bull. Math. Soc. Sci. Math. Roum. Tome 51(99)(3), 233–243 (2008)
Mirvakili, S., Anvariyeh, S.M., Davvaz, B.: On \(\alpha \)-relation and transitivity conditions of \(\alpha \). Commun. Algebra 36, 1695–1703 (2008)
Mirvakili, S., Davvaz, B.: Relations on Krasner \((m, n)\) -hyperrings. Eur. J. Comb. 31, 790–802 (2010)
Mirvakili, S., Davvaz, B.: Relationship between rings and hyperrings by using the notion of fundamental relations. Commun. Algebra 41(1), 70–82 (2013)
Mirvakili, S., Davvaz, B.: Applications of the \(\alpha ^*\) -relation to Krasner hyperrings. J. Algebra 362, 145–156 (2012)
Mousavi, S.S.H., Leoreanu-Fotea, V., Jafarpour, M.: \(\Re \)-parts in (semi)hypergroups. Ann. Math. Pure Appl. (4) 190, 667–680 (2011)
Vougiouklis, T.: The fundamental relation in hyperrings. The general hyperfield. Proceedings of 4th International Congress on Algebraic Hyperstructures and Applications (AHA 1990), World Scientific, Singapore, pp. 203–211 (1991)
Vougiouklis, T.: Hyperstructures and Their Representations, vol. 115. Hadronic Press Inc, Palm Harber (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mirvakili, S., Anvariyeh, S.M. & Davvaz, B. Rings derived from strongly \(\mathcal {U}\)-regular relations. Bol. Soc. Mat. Mex. 24, 107–121 (2018). https://doi.org/10.1007/s40590-016-0157-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40590-016-0157-z