Composition hyperrings

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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.

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

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

[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.

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

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

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

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

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

[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.

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

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

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

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

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

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

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

[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.

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

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

[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.

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

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

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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