TITLE:
Near-Vector Spaces Constructed over Zp, for p a Prime
AUTHORS:
Kelone Tefoetsile, Jeromy Kalunga, Mathews Zimba, James Muchinga, Saviour Chibeti, Henry M. Phiri
KEYWORDS:
Vector Spaces, Near Vector Spaces, Regularity, Compatibility, Fields, Near-Fields, F-Group and Quasi-Kernel
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.1,
January
28,
2023
ABSTRACT: The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Zp 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.