Browsing by Author "De Bruyn, Aletta"

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    Near vector spaces
    (Stellenbosch : Stellenbosch University, 1990) De Bruyn, Aletta; Van der Walt, A. P. J.; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences.
    ENGLISH ABSTRACT: The preliminary material in Chapter 1 is included in order that this work be reasonably self-contained. The main aim of this thesis is to give an exposition of the theory of near vector spaces, as introduced by J. Andre [1]. This is done in the second chapter. Concepts such as an F-group and its quasi-kernel are defined and investigated. A near vector space is then defined in terms of these notions, after which the theory of near vector spaces is developed. Three examples are given in Chapter 3. Their quasi-kernels are investigated and, in each case, it is shown that the near vector space under consideration is not a vector space. Finally, in the fourth chapter, certain known results concerning linear transformations of finite-dimensional vector spaces are recalled. These notions are then investigated for certain near linear transformations of a 2-dimensional near vector space.