A note on hypervector spaces

Sanjay Roy; Tapas K. Samanta

Discussiones Mathematicae - General Algebra and Applications (2011)

  • Volume: 31, Issue: 1, page 75-99
  • ISSN: 1509-9415

Abstract

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The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.

How to cite

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Sanjay Roy, and Tapas K. Samanta. "A note on hypervector spaces." Discussiones Mathematicae - General Algebra and Applications 31.1 (2011): 75-99. <http://eudml.org/doc/276586>.

@article{SanjayRoy2011,
abstract = {The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.},
author = {Sanjay Roy, Tapas K. Samanta},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {hyperoperation; hyperfield; hypervector spaces; linear dependent; linear independent; linear dependence; linear independence},
language = {eng},
number = {1},
pages = {75-99},
title = {A note on hypervector spaces},
url = {http://eudml.org/doc/276586},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Sanjay Roy
AU - Tapas K. Samanta
TI - A note on hypervector spaces
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2011
VL - 31
IS - 1
SP - 75
EP - 99
AB - The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.
LA - eng
KW - hyperoperation; hyperfield; hypervector spaces; linear dependent; linear independent; linear dependence; linear independence
UR - http://eudml.org/doc/276586
ER -

References

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  2. [2] F. Marty, Role de la notion d'hypergroupe dans l'étude des groupes non abéliens, Comptes Renclus Acad. Sci. Paris Math. 201 (1935), 636-638. Zbl61.1014.04
  3. [3] F. Marty, Sur les groupes et hypergroupes attachés à une fraction rationnelle, Ann. Sci. de l'Ecole Norm. Sup. 53 (3) (1936), 82-123. Zbl0014.10403
  4. [4] F. Marty, Sur une généralisation de la notion de groupe., in: pages 45-49, '8ème congrès des Mathématiciens Scandinaves', Stockholm 1934. Zbl61.1014.03
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  8. [8] M.S. Tallini, A-ipermoduli e spazi ipervettoriali, Rivista di Mat. Pura e Applicata, Universita' di Udine 3 (1988), 1-46. 
  9. [9] M.S. Tallini, Hypervector spaces, Fourth Int. Congress on AHA, Xanthi, Greece (1990), 167-174. Zbl0801.20057
  10. [10] M.S. Tallini, Spazi ipervettoriali fortemente distributivi a sinistra, Rend. Mat. Univ. Roma La Sapienza 11 (VII) (1991), 1-16. 
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  12. [12] M.S. Tallini, La categoria degli spazi ipervettoriali, Quaderni Sem. Geom. Comb. Dip. Mat. 'G. Castelnuovo' Univ. Di Roma La Sapienza, 110 (1993), 1-17. 
  13. [13] M.S. Tallini, Spazi ipervettoriali deboli e norme in tali spazi. Quaderni Sem. Geom. Comb. Dip. Mat. 'G. Castelnuovo', Univ. Di Roma La Sapienza, 111 (1993), 1-14. 
  14. [14] M.S. Tallini, La categoria degli spazi ipervettoriali, Rivista di Mat. Pura e Applicata, Univ. di Udine, 15 (1994), 97-109. 
  15. [15] M.S. Tallini, Weak hypervector spaces and norms in such spaces, Proc. Int. Congress Algebraic Hyperstructures and Applications, Iasi, Romania, Luglio 1993, Hadronic Press, Palm Harbor, Florida (U.S.A.) (1994), 109-206. 
  16. [16] M.S. Tallini, Characterization of Remarkable Hypervector spaces, Proc. of 8th int. Congress on Algebraic Hyperstructures and Applications, Samotraki, Greece, Sept. 1-9 2002, Spanidis Press, Xanthi, Greece, ISBN 960-87499-5-6 (2003), 231-237. Zbl1036.15003

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