## Publicacions Matemàtiques

### On rings with finite number of orbits

#### Abstract

Let $R$ be an associative unital ring with the unit group $U(R)$. Let $\mathcal{S}$ denote one of the following sets: the set of elements of $R$, of left ideals of $R$, of principal left ideals of $R$, or of ideals of $R$. Then the group $U(R)\times U(R)$ acts on the set $\mathcal{S}$ by left and right multiplication. In this note we are going to discuss some properties of rings $R$ with a finite number of orbits under the action of $U(R)\times U(R)$ on $\mathcal{S}$.

#### Article information

Source
Publ. Mat., Volume 58, Number 1 (2014), 233-249.

Dates
First available in Project Euclid: 20 December 2013