Construction of (M, N)-hypermodule over (R, S)-hyperring

S. Mirvakili; S. M. Anvariyeh; B. Davvaz

doi:10.2478/ausm-2019-0011

Abstract

The aim of this paper is to introduce a new class of hyper-modules that may be called (M, N)-hypermodules over (R, S)-hyperrings. Then, we investigate some properties of this new class of hyperstructures. Since the main tools in the theory of hyperstructures are the fundamental relations, we give some results about them with respect to the fundamental relations.

References

[1] S. M. Anvariyeh, B. Davvaz, Strongly transitive geometric spaces associated to hypermodules, J. Algebra, 322 (2009), 1340–1359.10.1016/j.jalgebra.2009.05.014
Search in Google Scholar Back to article
[2] S. M. Anvariyeh, S. Mirvakili, B. Davvaz, θ*- Relation on hypermodules and fundamental modules over commutative fundamental rings, Comm. Algebra, 36 (2) (2008), 622–631.10.1080/00927870701724078
Search in Google Scholar Back to article
[3] S. M. Anvariyeh, B. Davvaz, On the heart of hypermodules, Math. Scand., 106 (2010), 39–49.10.7146/math.scand.a-15123
Search in Google Scholar Back to article
[4] P. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani editor, 1993.
Search in Google Scholar Back to article
[5] P. Corsini, V. Leoreanu, Applications of hyperstructures theory, Advances in Mathematics, Kluwer Academic Publisher, 2003.10.1007/978-1-4757-3714-1
Search in Google Scholar Back to article
[6] B. Davvaz, M. Karimian, On the γ_n-complete hypergroups and K_H hypergroups, Acta Math. Sin. (Engl. Ser.), 24 (2008), 1901–1908.10.1007/s10114-008-6141-4
Search in Google Scholar Back to article
[7] B. Davvaz, M. Karimian, On the rn*$r_n^*$-complete hypergroups, European J. Combin., 28 (2007), 86–93.10.1016/j.ejc.2004.09.007
Search in Google Scholar Back to article
[8] B. Davvaz, V. Leoreanu-Fotea, Hyperring theory and applications, International Academic Press, USA, 2007.
Search in Google Scholar Back to article
[9] B. Davvaz, T. Vougiouklis, Commutative rings obtained from hyperrings (H_v-rings) with α*-relations, Comm. Algebra, 35 (2007), 3307–3320.10.1080/00927870701410629
Search in Google Scholar Back to article
[10] M. De Salvo, (H, G)−hypergroup, Riv. Mat. Uni. Parma, 4 (10) (1984), 207–216.10.3406/ecmed.1984.1603
Search in Google Scholar Back to article
[11] D. Freni, A new characterization of the derived hypergroup via strongly regular equivalences, Comm. Algebra, 30 (8) (2002), 3977–3989.10.1081/AGB-120005830
Search in Google Scholar Back to article
[12] M. Koskas, Groupoides, Demi-hypergroupes et hypergroupes, J. Math. Pures et Appl., 49 (1970), 155–192.
Search in Google Scholar Back to article
[13] S. Mirvakili, S. M. Anvariyeh, B. Davvaz, On α-relation and transitivity conditions of α, Comm. Algebra, 36 (2008), 1695–1703.10.1080/00927870801937364
Search in Google Scholar Back to article
[14] S. Spartalis, (H, R)-Hyperrings, Proc. Fourth Int. Congress on Algebraic Hyperstructures and Applications (Xanthi/Greece 1990), World Scientific Publ., (1991), 187–195.
Search in Google Scholar Back to article
[15] T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, Proc. Fourth Int. Congress on Algebraic Hyperstructures and Applications (Xanthi/Greece 1990), World Scientific Publ., (1991), 203–211.10.1142/9789814539555
Search in Google Scholar Back to article
[16] T. Vougiouklis, Hyperstructures and their representations Hadronic press Inc, USA, 1994.
Search in Google Scholar Back to article
[17] J. Zhan, B. Davvaz, K. P. Shum, Isomorphism theorems of hypermodules, Acta Math. Sinica (Chin. Ser.), 50 (2007), 909–914.
Search in Google Scholar Back to article

Construction of (M, N)-hypermodule over (R, S)-hyperring

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