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Near-Vector Spaces Constructed over Z<sub><i>p</i></sub>, for <i>p</i> a Prime
Department of Mathematics and Statistical Sciences, Bostwana International University of Science and Technology, Palaype, Botswana
Department of Mathematics, Copperbelt University, Kitwe, Zambia
Department of Mathematics, Copperbelt University, Kitwe, Zambia
Departrment of Natural Science, Levy Mwanawasa Medical University, Lusaka, Zambia
Economics Department, University of Lusaka, Lusaka, Zambia
Economics Department, University of Lusaka, Lusaka, Zambia
- 1 Department of Mathematics and Statistical Sciences, Bostwana International University of Science and Technology, Palaype, Botswana
- 2 Department of Mathematics, Copperbelt University, Kitwe, Zambia
- 3 Department of Mathematics, Copperbelt University, Kitwe, Zambia
- 4 Departrment of Natural Science, Levy Mwanawasa Medical University, Lusaka, Zambia
- 5 Economics Department, University of Lusaka, Lusaka, Zambia
- 6 Economics Department, University of Lusaka, Lusaka, Zambia
Advances in Pure Mathematics·Volume 13 (2023)·Pages 11–33·Published 19 January 2023·DOI10.4236/apm.2023.131002
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Abstract
The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z p for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.
KeywordsVector SpacesNear Vector SpacesRegularityCompatibilityFieldsNear-FieldsF-Group and Quasi-Kernel
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