Kajian Basis dan Dimensi pada Ruang Hipervektor Atas Lapangan

Abstract

The concept of algebraic hyperstructure is a generalisation of the concept of algebraic structure. The concept of algebraic hyperstructure discussed in this study is hypervector space. The purpose of this paper is to study the basis and dimension of the hypervector space. In hypervector space there is a strong left distributive property, namely (a+b)∘x=a∘x+b∘x, ∀a,b∈K,∀x∈V. In addition, in a hypervector space that has the K-invertible property, the importance of the strong left distribution property and the invertible property in this hypervector space ensures that each linearly independent set has no more than n elements, where n is the dimension of the hypervector space. Furthermore, the addition of vectors from outside the base will result or not linearly independent.

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