Open Access
2014 On rings with finite number of orbits
Małgorzata Hryniewicka, Jan Krempa
Publ. Mat. 58(1): 233-249 (2014).


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 $\mathcal{S}$.


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Małgorzata Hryniewicka. Jan Krempa. "On rings with finite number of orbits." Publ. Mat. 58 (1) 233 - 249, 2014.


Published: 2014
First available in Project Euclid: 20 December 2013

zbMATH: 1297.16034
MathSciNet: MR3161517

Primary: 16L30 , 16P99 , 16U60

Keywords: $U(R)$-orbits , Groups of units , semilocal rings , semiprimary rings

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. 1 • 2014
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