Edyta Bartnicka

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20152020

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4 papers · 1 filter

math.RA2020

Orbits of Free Cyclic Submodules over Rings of Lower Triangular Matrices

Edyta Bartnicka

Given a ring $T_{n}, n ⩾ 2$ , of lower triangular $n \times n$ matrices with entries from an arbitrary field $F$ , a complete description is performed of the orbits of free cycli…

math.RA2019

Affine and Projective Planes Linked with Projective Lines over Certain Rings of Lower Triangular Matrices

Edyta Bartnicka, Metod Saniga

Let $T_{n} (q)$ be the ring of lower triangular matrices of order $n \geq 2$ with entries from the finite field $F (q)$ of order $q \geq 2$ and let $^{2} T_{n} (q)$ denote its free left mo…

math.RA2017

The distant graph of the projective line over a finite ring with unity

Edyta Bartnicka, Andrzej Matras

We discuss the projective line $P (R)$ over a finite associative ring with unity. $P (R)$ is naturally endowed with the symmetric and anti-reflexive relation "dista…

math.RA2015

Free cyclic submodules in the context of the projective line

Edyta Bartnicka, Andrzej Matras

We discuss the free cyclic submodules over an associative ring $R$ with unity. Special attention is paid to those, which are generated by outliers. This paper describes all orbits…