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On Dimension of Hypervector Spaces

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2008

Key Words:

Author NameUniversity of Author

AMS Codes:

Abstract (2. Language): 
The purpose of this paper is the study of dimension of hypervector spaces. In this regard first we introduce the notions of linear independent (resp. dependent) and basis of hypervector spaces. Then we study the properties of hypervector spaces and prove that under certain conditions dimension for such spaces there exist. Finally, we use the fundamental relation on hypervector spaces to construct a functor from the category of hypervector spaces over a fixed field K and the category of classical vector spaces over K, and we will prove that this functor preserves dimension.
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  • 2
32-50
  • English

REFERENCES

References: 

[1] R. Ameri, Fuzzy Hypervector Spaces over Valued Fields, Iranian Journal of Fuzzy Systems, 2: 37-47
(2005).
[2] R. Ameri, On Categories of Hypergroups and Hypermodules, Journal of Discrete Mathematical Science
and Cryptography, 6, 2-3: 121-132 (2003).
[3] P. Corsini, Prolegomena of Hypergroup Theory, Second Edition, Aviani Editor, 1993.
[4] P. Corsini, V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Academic Publications,
2003.
[5] F. Marty, Sur une generalization de la notion de groupe, 8th congress des Mathematiciens Scandinaves,
Stockholm 45-49 (1934).
[6] M. S. Tallini, Hypervector Spaces, Proceedings of the Fourth International Congress on Algebraic
Hyperstructures and Applications, Xanthi, Greece, 167-174 (1990).
[7] M. S. Tallini, Weak Hypervector Spaces and Norms in such Spaces, Proceedings of the Fifth International
Congress on Algebraic Hyperstructures and Applications, Jasi, Rumania, Hadronic Press,
199-206 (1994).
[8] M. S. Tallini, Matroidal Hypervector Spaces, Journal of Geometry, 42: 132-140 (1991).
REFERENCES 50
[9] G. Tallini, Dimentions in Multivalued Algebraic Structures, Italian Journal of Pure and Applied Mathematics,
1: 51-64 (1997).
[10] T. Vougiuklis, Hyperstructures and their Representations, Hadronic Press, Inc., 1994.
[11] T. Vougiuklis, HV -Vector Spaces, Proceedings of the Fifth International Congress on Algebraic Hyperstructures
and Applications, Jasi, Rumania, Hadronic Press, 181-190 (1994).
[12] M. M. Zahedi, R. Ameri, On the Prime, Primary and Maximal Subhypermodules, Italian Journal of
Pure and Applied Mathematics, 5: 61-80 (1999).

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