Free Cyclic Submodules and Non-Unimodular Vectors
Combinatorics
2011-08-12 v2 Mathematical Physics
math.MP
Abstract
Given a finite associative ring with unity, , and its two-dimensional left module, , the following two problems are addressed: 1) the existence of vectors of that do not belong to any free cyclic submodule (FCS) generated by a unimodular vector and 2) conditions under which such (non-unimodular) vectors generate FCSs. The main result is that for a non-unimodular vector to generate an FCS of , must have at least two maximal right ideals of which at least one is non-principal.
Cite
@article{arxiv.1107.3050,
title = {Free Cyclic Submodules and Non-Unimodular Vectors},
author = {Joanne L. Hall and Metod Saniga},
journal= {arXiv preprint arXiv:1107.3050},
year = {2011}
}
Comments
8 pages, no figures; V2 - some theorems slightly reworked, text polished and a reference added