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arXiv · 2305.13319

The distributive elements of a near-field

Julien Bahimuzi
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Abstract

In this thesis, we investigated some properties of (left)near fields and derived some results. We are focusing on $D(\alpha, \beta)$ which is the generalized set of distributive elements of a nearfield. In particular, we investigated some conditions on $\alpha,\beta, \alpha+\beta$ for $D(\alpha, \beta)$ to be a subfield of $\mathbb{F}_{q^{n}}$. In nearfield theory the two distributive laws can not hold at the same time. So in term of left nearfield and near-ring, the right distributivity does not hold and to solve the problem, we defined a set of all distributive elements called $D(R)$.

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Julien Bahimuzi. 2023-05-13. The distributive elements of a near-field. https://arxiv.org/abs/2305.13319

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