On generalizations of vector and Banach spaces by hyperstructres

Document Type : Research Paper

Authors

1 Department of mathematics, University of Hormozgan, Hormozgan, Bandar abbas, Iran.

2 Institute of Mathematics,Yunnan University, Kunming, 650091, P.R. China

Abstract

In this paper,  we generalize the vector space by considering the group as a canonical $m$-ary hypergroup, the field as a Krasner $(m,n)$-hyperfield. Moreover, we define  the $m$-ary hyper Banach spaces and  investigate some of their related properties.

Keywords

References

[1] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics vol.5 Kluwer Academic Publishers Dordrecht (2003).
[2] P. Corsini, Prolegomena of hypergroup theory, Second Edition, Aviani Editore (1993).
[3] B. Davvaz and V. Leoreanu-Fotea, Hyperring theory and applications, International Academic Press USA (2007).
[4] B. Davvaz and T. Vougiouklis, n-ary hypergroups, Iran. J. Sci. Technol. Trans. A 30 (A2) (2006) 165-174.
[5] B. Davvaz, W.A. Dudek and S. Mirvakili, Neutral elements, fundamental relations and n-ary hypersemigroups, Internat. J. Algebra Comput. 19 (4) (2009) 567-583.
[6] B. Davvaz, Wieslaw A. Dudek and T. Vougiouklis, A generalization of n-ary algebraic systems, Comm. Algebra 37 (2009) 1248-1263.
[7] W. D¨ornte, Unterschungen uber einen verallgemeinerten gruppenbegriff, Math. Z. (1929) 29 1-19.
[8] W.A. Dudek and K. Glazek, Around the Hosszu Gluskin theorem for n-ary groups, Discrete Math. 308 (2008) 4861-4876.
[9] W.A. Dudek and I. Grozdzinska On ideals in regular n-semigroups, Mat. Bilten 29 (1980) 29-30.
[10] M. Ghadiri and B. N. Waphare, n-ary polygroups, Iran. J. Sci. Technol. Trans. A Sci. 33 (2009) 2, 145-158.
[11] V. Leoreanu-Fotea and B. Davvaz, Roughness in n-ary hypergroups, Inform. Sci 178 (2008) 4114-4124.
[12] V. Leoreanu-Fotea and B. Davvaz, n-hypergroups and binary relations, Eur. J. Combin. 29 (2008) 1027- 1218.
[13] V. Leoreanu-Fotea and B. Davvaz, n-hypergroups and binary relations, Eur. J. Combin. 29 (5) (2008) 1207-1218
Algebraic Structures and Their Applications
Volume 7, Issue 2
November 2020
Pages 163-177

Files

Share

How to cite

Statistics