References
- [1] Abbasizadeh, N., Cristea, I., Davvaz, B., Zhan, J. Subpolygroups related to a fuzzy topology, Journal of Multiple-Valued Logic and Soft Computing 31(1-2), 155–173, 2018.
- [2] Abbasizadeh, N., Davvaz, B., Leoreanu-Fotea, V. Studies on fuzzy topological polygroups, Journal of Intelligent and Fuzzy Systems, 32 (1), 1101–1110, 2017, doi: 10.3233/JIFS-16244.10.3233/JIFS-16244
- [3] Aghabozorgi, H., Davvaz, B., Jafarpour, M. Solvable Polygroups and Derived Subpolygroups, Communications in Algebra, 41 (8), 3098–3107, 2013, doi: 10.1080/00927872.2012.66100610.1080/00927872.2012.661006
- [4] Ameri, R., Hoskova-Mayerova, S., Fuzzy Continuous Polygroups, In: Aplimat - 15th Conference on Applied Mathematics 2016 Proceedings. Bratislava: Vydavatelstvo STU - Slovak University of Technoology in Bratislava, 13–19, 2016.
- [5] Ameri, R., Aivazi, M., Hoskova-Mayerova, S. Superring of polynomials over a hyperring, Mathematics 2019, 7, 902; doi:10.3390/math7100902.10.3390/math7100902
- [6] Chvalina J., Hoskova-Mayerova, S.., Deghan Nezhad, A. General actions of hypergroups and some applications, An. Stiint. Univ. Ovidius” Constanta Ser. Mat., 21(1), 59–82, 2013.10.2478/auom-2013-0004
- [7] Connes, A., Consani, C. From monoids to hyperstructures: in search of an absolute arithmetic, Casimir Force, Casimir Operators and the Riemann Hypothesis, de Gruyter, 147–198, 2010.10.1515/9783110226133.147
- [8] Connes, A., Consani, C. The hyperring of adele classes, Journal of Number Theory, 131(2), 159–194, 2011.10.1016/j.jnt.2010.09.001
- [9] Connes, A., Consani, C. The universal thickening of the field of real numbers, in: A. Alaca (ed.) et al., Advances in the Theory of Numbers. Proceedings of the Thirteenth Conference of the Canadian Number Theory Association, 11-74, Fields Institute Communications 77, Springer, New York, 2015.10.1007/978-1-4939-3201-6_2
- [10] Comer, S. D. Polygroups derived from cogroups, Journal of Algebra, 89 (2), 397–405, 1984, doi: 10.1016/0021-8693(84)90225-4.10.1016/0021-8693(84)90225-4
- [11] Corsini, P. Prolegomena of Hypergroup Theory, Aviani Editore, Tricesimo, 1993.
- [12] Corsini, P., Leoreanu, V. Applications of Hyperstructure Theory, Kluwer Academical Publications, Dordrecht, 2003.10.1007/978-1-4757-3714-1
- [13] Cristea, I., Stefanescu, M., Angheluta, C. About the fundamental relations defined on the hypergroupoids associated with binary relations, European Journal of Combinatorics 32(1), 72–81, 2011.10.1016/j.ejc.2010.07.013
- [14] Davvaz, B., Leoreanu-Fotea, V. Hyperring Theory and Applications, International Academic Press, USA, 2007.
- [15] B. Davvaz, Cristea, I. Fuzzy Algebraic Hyperstructures, Studies in Fuzziness and Soft Computing 321, Springer International Publishing 2015, doi: 10.1007/978-3-319-14762-8.10.1007/978-3-319-14762-8
- [16] De la Harpe, P. Topics in geometric group theory. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2000.
- [17] Freni, D. Strongly Transitive Geometric Spaces: Applications to Hyper-groups and Semigroups Theory, Communications in Algebra, 32(3), 969–988, 2004.10.1081/AGB-120027961
- [18] Gladki, P., Marshall, M. Orderings and signatures of higher level on multi-rings and hyperfields, Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology, 10(03), 489-518, 2012.10.1017/is012004021jkt189
- [19] Hoskova-Mayerova S., Chvalina, J. A survey of investigations of the Brno research group in the hyperstructure theory since the last AHA Congress, In:10th International Congress on Algebraic Hyperstructures and Applications AHA 2008, 2009, Univ Defence, Brno, Czech Republic, 71–84.
- [20] Izhakian, Z., Knebusch, M., and Rowen, L. Layered tropical mathematics, Journal of Algebra, 416, 200–273, 2014.10.1016/j.jalgebra.2014.05.019
- [21] Izhakian, Z., Rowen, L. Supertropical algebra, Advances in Mathematics, 225(4), 2222–2286, 2010.10.1016/j.aim.2010.04.007
- [22] Jafarpour, M., Mousavi, S. Sh., Leoreanu, V., Jantani, F. On 2-strongly transitive geometric spaces, J Algebra Appl. 17(08), 1850140, (2018) doi.org/10.1142/S0219498818501402.10.1142/S0219498818501402
- [23] Jun, J. Algebraic geometry over semi-structures and hyper-structures of characteristic one, PhD thesis, Johns Hopkins University, Baltimore, Maryland, USA, May 2015.
- [24] Jun, J. Valuations of semirings, J Pure Appl Algebra 222 (8), 2063-2088.10.1016/j.jpaa.2017.08.020
- [25] Loh, C. Geometric group theory: An introduction, Springer International Publishing AG, 2018.
- [26] Lorscheid, O. The geometry of blueprints: Part i: Algebraic background and scheme theory, Advances in Mathematics, 229(3), 1804–1846, 2012.10.1016/j.aim.2011.12.018
- [27] Lorscheid, O. Scheme theoretic tropicalization, arXiv preprint arXiv:1508.07949, 2015.
- [28] Marshall, M. Real reduced multirings and multifields, Journal of Pure and Applied Algebra, 205(2), 452–468, 2006.10.1016/j.jpaa.2005.07.011
- [29] Marty, F. Sur une Generalization de la Notion de Groupe, 8th Congress Math. Scandenaves, Stockholm, Sweden, 45–49, 1934.
- [30] Mirvakili, S., and Davvaz, B. Strongly transitive geometric spaces: Applications to hyperrings, Revista de la Union Mathematica Argentina, 53(1), 43–53, 2012.
- [31] Sisto, A. Lecture notes on Geometric Group Theory, Under construction, July 3, 2014.
- [32] Viro, O. Hyperfields for tropical geometry I. Hyperfields and dequantization, arXiv:1006.3034, 47p., 2010.
- [33] Viro, O. On basic concepts of tropical geometry, Proceedings of the Steklov Institute of Mathematics, 273(1),252–282, 2011.10.1134/S0081543811040134
- [34] Vougiouklis, T., Hyperstructures and Their Representations, Hadronic Press, Palm Harbor, FL, 1994.
- [35] Yaqoob, N., Cristea, I., Gulistan, M., Nawaz, S. Left Almost Polygroups, Italian Journal of Pure and Applied Mathematics, 39, 465-474, 2018.
- [36] Zhan, J., Mousavi, S. Sh., Jafarpour, M. On Hyperactions of Hypergroups, U.P.B. Sci. Bull., Series A, 73(1), 117-128, 2011.