Geodesic
A note on hypervector spaces
Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 1, pp. 75-99

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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.
Keywords: hyperoperation, hyperfield, hypervector spaces, linear dependent, linear independent 
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Roy, Sanjay; Samanta, Tapas. A note on hypervector spaces. Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 1, pp. 75-99. http://geodesic.mathdoc.fr/item/DMGAA_2011_31_1_a4/