The subspace structure of finite dimensional Beidleman near-vector spaces

TL;DR

This paper explores the subspace structure of finite dimensional Beidleman near-vector spaces, providing classifications, algorithms, and characterizations to deepen understanding of their algebraic properties.

Contribution

It introduces a classification of finite dimensional Beidleman near-vector spaces and an algorithm to compute minimal R-subgroups, advancing the algebraic theory of these spaces.

Findings

Classification of finite dimensional Beidleman near-vector spaces

Algorithm for computing smallest R-subgroup containing a set

Complete classification of subspaces in these spaces

Abstract

The subspace structure of Beidleman near-vector spaces is investigated. We characterise finite dimensional Beidleman near-vector spaces and we classify the R-subgroups of finite dimensional Beidleman near-vector spaces. We provide an algorithm to compute the smallest R-subgroup containing a given set of vectors. Finally, we classify the subspaces of finite dimensional Beidleman near-vector spaces.