Free hypermodules: a categorical approach

References

• Adamek, J., Herrlich, H., Strecker, G. E. (1990). Abstract and Concrete Categories. New York: John Wiley and Sons, Inc.
   Google Scholar
• Al Tahan, M., Davvaz, B. (2017). On the existence of hyperrings associated with arithmetic functions. J. Number Theory 174:136–149. DOI: 10.1016/j.jnt.2016.10.017.
   Web of Science ®Google Scholar
• Al Tahan, M., Hoskova-Mayerova, S., Davvaz, B. (2018). An overview of topological hypergroupoids. J. Intell. Fuzzy Syst. 34(3):1907–1916. DOI: 10.3233/JIFS-171265.
   Web of Science ®Google Scholar
• Anvariyeh, S. M., Mirvakili, S., Davvaz, B. (2008). θ*-Relation on hypermodules and fundamental modules over commutative fundamental rings. Commun. Algebra 36(2):622–631. DOI: 10.1080/00927870701724078.
   Web of Science ®Google Scholar
• Borceux, F. (1994). Handbook of categorical algebra. Basic Category Theory, Vol. 1. Cambridge: Cambridge University Press.
   Google Scholar
• Borceux, F. (1994). Handbook of categorical algebra. Categories and Structures, Vol. 2. Cambridge: Cambridge University Press.
   Google Scholar
• Connes, A., Consani, C. (2010). From monoids to hyperstructures. In: Gerrit Dijk, Masato Wakayama, eds. Search of an Absolute Arithmetic, Casimir Force, Casimir Operators and the Riemann Hypothesis. Berlin: de Gruyter, pp. 147–198.
   Google Scholar
• Connes, A., Consani, C. (2011). The hyperring of Adele classes. J. Number Theory 131(2):159–194. DOI: 10.1016/j.jnt.2010.09.001.
   Web of Science ®Google Scholar
• Connes, A., Consani, C. (2015). The universal thickening of the field of real numbers. In: Alaca, A., Alaca, S., Williams, K. S., eds. Advances in the Theory of Numbers. Proceedings of the Thirteenth Conference of the Canadian Number Theory Association. Fields Institute Communications 77, New York: Springer, pp. 11–74.
   Google Scholar
• Corsini, P., Leoreanu, V. (2003). Applications of Hyperstructure Theory. Dordrecht: Kluwer Academical Publications.
   Google Scholar
• Davvaz, B., Cristea, I. (2015). Fuzzy Algebraic Hyperstructures. Studies in Fuzziness and Soft Computing, Vol. 321. Cham: Springer International Publishing. DOI: 10.1007/978-3-319-14762-8.
   Google Scholar
• Davvaz, B., Leoreanu-Fotea, V. (2007). Hyperring Theory and Applications. Palm Harbor, FL: International Academic Press.
   Google Scholar
• Davvaz, B., Vougiouklis, T. (2007). Commutative-rings obtained from hyperrings (Hv-rings) with α*-relations. Commun. Algebra 35:3307–3320. DOI: 10.1080/00927870701410629.
   Web of Science ®Google Scholar
• Hošková, Š., Chvalina, J. (2008). A survey of investigations of the Brno research group in the hyperstructure theory since the last AHA Congress, AHA. Published 2009, ISBN: 978-80-7231-688-5, p. 71–84.
   Google Scholar
• Hosseini, S. N., Mousavi, S. S., Zahedi, M. M. (2002). Category of polygroup objects. Bull. Iranian Math. Soc. 28:67–86.
   Google Scholar
• Kelly, G. M., Street, R. (1974). Review of the elements of 2-categories. Springer LNM 420. : Springer Verlag. pp. 75–103.
   Google Scholar
• Krasner, M. (1983). A class of hyperrings and hyperfields. Int. J. Math. Math. Sci. 6(2):307–311. DOI: 10.1155/S0161171283000265.
   Google Scholar
• Mac Lane, S. (1998). Homology, 2nd ed. Berlin-New York: Springer-Verlag.
   Google Scholar
• Marty, F. (1934). Sur Une Generalization de la Notion de Groupe, Proc. 8th Congress Math. Scandinavia, Stockholm, Sweden, p. 45–49.
   Google Scholar
• Massouros, C. G. (1988). Free and cyclic hypermodules. Annali di Matematica Pura ed Applicata. Serie. 150(1):153–166. DOI: 10.1007/BF01761468.
   Google Scholar
• Mousavi, S. S., Jafarpour, M. (2011). On free and weak free (semi)hypergroups. Algebra Colloq. 18(spec01):873–880. DOI: 10.1142/S1005386711000757.
   Google Scholar
• Shojaei, H., Ameri, R., Hoskova-Mayerova, S. (2018). On properties of various morphisms in the categories of general Krasner hypermodules. Italian J. Pure Appl. Math. 39:475–484.
   Google Scholar