The distributive elements of a near-field

2023/05/13 by Julien Bahimuzi, Bahimuzi, Julien
Physics and Astronomy · #12K05 #16Y30 #Advanced Differential Geometry Research #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2305.13319

openalex publication_date 2023/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this thesis, we investigated some properties of (left)near fields and derived some results. We are focusing on D(α, β) which is the generalized set of distributive elements of a nearfield. In particular, we investigated some conditions on α,β, α+β for D(α, β) to be a subfield of \mathbbF_qⁿ. 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).

Related

• On the generalized distributive set of a finite nearfield
• Distribution and Generalized Center in Planar Nearrings
• Near-field structures on a given scalar group
• Distributive decomposition of near-vector spaces
• Units in Near-rings