Orbits of Free Cyclic Submodules over Rings of Lower Triangular Matrices

Edyta Bartnicka

paper

Orbits of Free Cyclic Submodules over Rings of Lower Triangular Matrices

arXiv:2002.04325

Abstract

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 cyclic submodules of $^{2} T_{n}$ , under the action of the general linear group $G L_{2} (T_{n})$ . It is given its total number, which is equal to the Bell number $B_{n}$ , and there are shown their representatives.