Construction of composition (m, n, k)-hyperrings

Davvaz, B.; Rakhsh-Khorshid, N.; Shum, K. P.

doi:10.1515/auom-2016-0009

Abstract

In this paper, our aim is to introduce the notion of a composition (m, n, k)-hyperring and to analyze its properties. We also consider the algebraic structure of (m, n, k) hyperrings which is a generalization of composition rings and composition hyperrings. Also, the isomorphism theorems of ring theory are derived in the context of composition (m, n, k)-hyperrings.

References

[1] I. Adler, Composition rings, Duke Math. J., 29 (1962), 607-623.10.1215/S0012-7094-62-02961-7
Search in Google Scholar Back to article
[2] I. Cristea and S. Jančić-Rašović, Composition hyperrings, An. Şt. Univ. Ovidius Constanţa, 21(2) (2013), 81-94.10.2478/auom-2013-0024
Search in Google Scholar Back to article
[3] B. Davvaz, A new view of fundamental relations on hyperrings, Proceed- ings of 10th Int. Congress on Algebraic Hyperstructures and Applications, AHA 2008, pp. 43-55.
Search in Google Scholar Back to article
[4] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007.
Search in Google Scholar Back to article
[5] B. Davvaz, W.A. Dudek and T. Vougiouklis, A generalization of n-ary algebraic systems, Comm. Algebra, 37(4) (2009), 1248-1263.10.1080/00927870802466835
Open DOI Search in Google Scholar Back to article
[6] B. Davvaz and T. Vougiouklis, n-ary hypergroups, Iran. J. Sci. Technol. Trans. A, 30(2) (2006), 165-174.
Search in Google Scholar Back to article
[7] S. Jančić-Rašović and V. Dašić, Some new classes of (m; n)-hyperrings, Faculty of Sciences and Mathematics, University of Nis, Serbia, 26(3) (2012), 585-596.10.2298/FIL1203585J
Search in Google Scholar Back to article
[8] M. Krasner, A class of hyperrings and hyperfields, International Journal of Mathematics and Mathematical Sciences, 2 (1983), 307-312.10.1155/S0161171283000265
Search in Google Scholar Back to article
[9] V. Leoreanu-Fotea, Canonical n-ary hypergroups, Italian. J. Pure Appl. Math., 24 (2008).
Search in Google Scholar Back to article
[10] S. Mirvakili and B. Davvaz, Constructions of (m; n)-hyperrings, Matematicki Vesnik, 67(1) (2015), 1-16.
Search in Google Scholar Back to article
[11] S. Mirvakili and B. Davvaz, Relations on Krasner (m; n)-hyperrings, European. J. Combin., 31 (2010), 790-802.10.1016/j.ejc.2009.07.006
Search in Google Scholar Back to article

Construction of composition (m, n, k)-hyperrings

Abstract

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