On Dimension of Hypervector Spaces

Authors

  • Reza Ameri University of Mazandaran, Babolsar,Iran
  • O.R. Dehghan University of Mazandaran, Babolsar, Iran

Keywords:

hypervector spaces, linearly independent, basis, dimension,

Abstract

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.

Author Biographies

  • Reza Ameri, University of Mazandaran, Babolsar,Iran
    Mathematics, Professor
  • O.R. Dehghan, University of Mazandaran, Babolsar, Iran

    Mathematics, Ph.d

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Published

2008-06-30

Issue

Vol. 1 No. 2: (April 2008)

Section

Algebra

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How to Cite

On Dimension of Hypervector Spaces. (2008). European Journal of Pure and Applied Mathematics, 1(2), 32-50. https://www.ejpam.com/index.php/ejpam/article/view/65