Representations on Raised Very Thin Hv-fields
محورهای موضوعی : Transactions on Fuzzy Sets and Systems
Thomas Vougiouklis
1
(School of Science and Education, Democritus University of Thrace, Greece.)
کلید واژه: hope, Hyperstructure, Hv-structure, Hv-group Hv-ring, Hv-field,
چکیده مقاله :
The hyperstructures have applications in mathematics and other sciences such as biology, physics, linguistics, sociology, to mention but a few. For this, mainly, the largest class of the hyperstructures, the Hv -structures, is used, which satisfy the weak axioms where the non-empty intersection replaces the equality and they are straightly related to fuzzy set theory. The fundamental relations connect the Hv -structures with the classical ones, moreover, they reveal new concepts as the Hv -fields. Hv -numbers are called the elements of an Hv -field and they are used in representation theory. We introduce the raised finite Hv -fields, and present some results and examples on 2 × 2 representations on them.
The hyperstructures have applications in mathematics and other sciences such as biology, physics, linguistics, sociology, to mention but a few. For this, mainly, the largest class of the hyperstructures, the Hv -structures, is used, which satisfy the weak axioms where the non-empty intersection replaces the equality and they are straightly related to fuzzy set theory. The fundamental relations connect the Hv -structures with the classical ones, moreover, they reveal new concepts as the Hv -fields. Hv -numbers are called the elements of an Hv -field and they are used in representation theory. We introduce the raised finite Hv -fields, and present some results and examples on 2 × 2 representations on them.
[1] P. Corsini and V. Leoreanu, Application of Hyperstructure Theory, Springer, Boston, (2003).
[2] P. Corsini and T. Vougiouklis, From groupoids to groups through hypergroups, Rend. Mat., 9 (1989), 173-181.
[3] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, (2007).
[4] B. Davvaz, R. M. Santilli and T. Vougiouklis, Multi-valued Hypermathematics for characterization of matter and antimatter systems, J. Comp. Meth. Sci. Eng. (JCMSE), 13 (2013), 37-50.
[5] B. Davvaz, S. Vougioukli and T. Vougiouklis, On the multiplicative Hv-rings derived from helix hyperoperations, Util. Math., 84 (2011), 53-63.
[6] B. Davvaz and T. Vougiouklis, A Walk Through Weak Hyperstructures, Hv-Structures, World Scientific, Singapore, (2019).
[7] D. Freni, Una nota sul cuore di un ipergruppo e sulla chiusura transitiva β∗di β, Rivista Mat. Pura Appl., 8 (1991), 153-156.
[8] M. Koskas, Groupoides, demi-groupoides et hypergroups, J. Math. Pures Appl., 49(9) (1970), 155-192.
[9] R. M. Santilli, Embedding of Lie-algebras into Lie-admissible algebras, Nuovo Cimento, 51 (1967), 570-576.
[10] R. M. Santilli, Studies on A. Einstein, B. Podolsky and N. Rosen argument that quantum mechanics is not a complete theory, I: Basic methods, Ratio Mathematica, 38 (2020), 5-69.
[11] R. M. Santilli and T. Vougiouklis, Isotopies, Genotopies, Hyperstructures and their Applications, New Frontiers in Mathematics, Hadronic Press, Palm Harbor, United States, (1996).
[12] T. Vougiouklis, Generalization of P-hypergroups, Rend. Circolo Mat. Palermo, Ser.II, 36 (1987), 114-121.
[13] T. Vougiouklis, The very thin hypergroups and the S-construction, Combinatorics88, Incidence Geom. Comb. Str., 2 (1991), 471-477.
[14] T. Vougiouklis, The fundamental relation in hyperrings, The general hyperfield, 4thAHA, Xanthi (1990), World Scientific, Singapore, (1991).
[15] T. Vougiouklis, Hyperstructures and their Representations, Monographs in Math., Hadronic, Palm Habor, United States, (1994).
[16] T. Vougiouklis, Some remarks on hyperstructures, Contemporary Math., Amer. Math. Society, 184 (1995), 427-431.
[17] T. Vougiouklis, On Hv-rings and Hv-representations, Discrete Math., 208/209, (1999), 615-620.
[18] T. Vougiouklis, The h/v-structures, Discrete Math., 6 (2003), 235-243.
[19] T. Vougiouklis, ∂-operations and Hv-fields, Acta Math. Sinica, Engl. Ser., 24 (2008), 1067-1078.
[20] T. Vougiouklis, From Hv-rings to Hv-fields, Int. J. Algebr. Hyperstructures. Appl., 1(1) (2014), 1-13.
[21] T. Vougiouklis, Hv-fields, h/v-fields, Ratio Mathematica, 33 (2017), 181-201.
[22] T. Vougiouklis, Fundamental Relations in Hv-structures, The Judging from the Results proof, J. algebr. hyperstrucres log. algebr., 1(1) (2020), 21-36.
[23] T. Vougiouklis, Minimal Hv-fields, Ratio Mathematica, 38 (2020), 313-328.
